This pie is the ultimate ode to Pi. A full sphere of crust filled with pudding gives you the perfect pi-inspired pie eating experience. The ratio of volume to surface area of a sphere is the highest possible for a closed shape. So a spherical pie creates the largest possible filling content relative to crust. It is the ultimate dessert experience for pi and pie lovers alike.

See more pictures and details on my blog entry here.
Serve this up alongside some sweet or savory Fried Pi Pies for a fantastic Pi Day celebration!

Step 1: Calculations and Considerations

First you need a pie crust mold. The crust will be a two-part crust, with each part being baked around semi-spherical object. You might have something around the house that's got a fantastic semi-circular shape but it should be made from an oven-worthy material. I am using a glass candle holder that has been cleaned thoroughly and has no wax residue. Since it is not tempered, it's important to be very careful and not to allow the glass to cool too quickly. So do not put it in the refrigerator, in your sub-zero detached garage, etc. to cool it faster. Just wait. If you choose glass, be careful! Do this at your own risk. (People will have issues with my use of non-tempered glass so this is for their satisfaction.)

Calculate the volume of filling. Measure around the widest part of the sphere. This is the circumference. If you don't have a flexible measuring tape, wrap a piece of string around it, mark it, and measure that. Use this to calculate the volume of your sphere. This sphere calculator will calculate the volume for you. A cup of pudding is approximately 14.5 square inches. My 11" diameter mold will result in 22.45 square inches, about 1 1/2 cups filling so I made two cups of filling.

I had an amazing semi-circular candle shade that was almost a perfect sphere with little holes for light and oxygen to go through. However, I calculated the volume of this 22" diameter sphere and it was a staggering 180 cubic inches requiring about 12 cups filling. This is why I went with a smaller mold.

Step 2: Supplies

For an 11" diameter sphere, you need:
crust mold (see the previous step, Calculations and Considerations, for a description of objects to use for this)
1 pie crust (for a single crust pie)
1 small (3.4 oz) box instant pudding mix
2 cups milk
3 oz. candy-making chocolate (almond bark or similar) -- I choose white chocolate
2 pastry bags and coupler with tips* (or zip top bag)
aluminum foil
pan to hold the crust mold
pastry brush
2 heavy glasses or mugs

*ideally, one tip will be flat and the other round. They aren't necessary but do make the process much simpler.

Step 3: Creating the Crust

Preheat the oven to 425 degrees.

Cover the crust mold in foil. This is done both because foil is food safe and because the foil makes it easier to remove the crust.

Divide the crust in half. Refrigerate one half and roll out the other half into at least an 8" circle. I rolled mine relatively thick, about 3/16" thick. Lay the crust over the foil-covered mold and smooth over the rounded surface.

Push together the folded areas or cut out excess dough and push the edges together with a little water to "glue" the seams. Trim off some of the obvious excess crust (important because it will cause the crust to sag as you trim it to the proper length).

To cut an even bottom edge to the semi-sphere, find an object about the same height as the cut. I used a pudding box but things like glasses might work for your cutting guide. Lay the knife on this object and mark around the edges, moving either the crust mold or the height guide as you work.

Use a fork or toothpick to poke holes in the crust to release air bubbles as it bakes.

Place the crust mold on a cookie sheet or other pan and bake 12-15 minute until lightly browned and cooked through.

A few minutes after it comes out of the oven, pull the crust off the mold. Invert it to allow moisture to come out of the inside of the crust. I find the inside of the crust is less soft if I remove the crust immediately. If it doesn't come off easily, wait until the whole thing is cool and pull the foil off the mold. Do not try to cool your crust mold by putting it somewhere cold if it is glass. It MUST cool naturally or you risk cracking or breaking it.

Once the entire crust mold is cool, repeat for the other side of the sphere.

Step 4: Preparing to Fill

Once both sides of the crust are cool, you need to make sure they fit together. The biggest obstacle is if the bottoms aren't flat. Set them on the counter to see if they are flat. If the bottoms aren't flat enough due to sagging while baking or a badly cut edge, use a microplaner or hard cheese grater to smooth them down like sandpaper until they sit flat.

Melt about 1oz chocolate according to package instructions and spread in the insides of both halves. It will seal the inside of the crust against the moisture from the pudding as well as provide structural support for the sphere. Place the two halves into two heavy glasses or mugs to prevent them from rolling. Refrigerate until the chocolate is firm, about 5-10 minutes, depending on the thickness of chocolate.

Step 5: Assembly

Mix the pudding according to the package and pour into the halves of the sphere. Refrigerate until set.

Select the side that will be the top. Melt an ounce of chocolate and place in your pastry bag or zip top bag. Either use a flat icing tip or else cut a small hole in the corner of the bag. Pipe a layer of white chocolate over the top half of the sphere. Be sure it fully covers the pudding and extends to the edges of the crust, touching the crust so it will create a pudding barrier. Realize that, for the first time in your life you've read the term "pudding barrier." Refrigerate until set, about 10 minutes.

Once the pudding barrier is set. Fill a piping bag or zip top bag with another ounce of melted chocolate. If your bag is still full of melted chocolate, by all means, use it instead of filling another bag. Using a round tip or a cut corner of the bag, pipe a thick layer of chocolate around the rim of the bottom half of the sphere. This should cover the edge of the crust. Then gently, turn the top side of your sphere over and place it onto the bottom. Using your finger to smooth the chocolate seam. Refrigerate another 10 minutes to ensure your sphere is sealed before serving.

Step 6: Cutting

The spherical pie might be perplexing to divide but it has been done successfully, and with pictorial evidence.

First, I got the knife hot by dipping it in hot water for a minute. Then I stabbed into the chocolate that joins both half spheres. I intended to saw through but I simply stabbed into this equator, twisted the knife slightly, and easily pried the sphere in half.

I used kitchen scissors to start the cuts that would divide the hemispheres in half and then slid my knife into the grooves from the scissors to finish the cut. I repeated it for the other side. I snapped the white chocolate disk (pudding barrier) into quarters and garnished each piece.