You may ask me, "Why puff pastry?", to which I answer, "Why not?".
Oh yeah, this is in the Pi Day contest. Happy Pi Day!
Step 1: Getting the pastry
I used frozen puff pastry sheets (Because 1) I cannot make this to save my life, and 2) I already had a box in my freezer from another project). But here is a good recipe (from The Essential Baking Cookbook) if you want to make your own:
You need 200--250g unsalted butter, 2 cups flour, 1/2 tsp salt, and 2/3 cup cold water.
1. Melt 30g of the butter in a saucepan. Sift the flour and salt onto a work surface and make a well in the center. Add the melted butter and water to the center and blend with your fingertips, gradually drawing in the flour. You should end up with a crumb mixture- if it seems a little dry, add extra drops of water before bringing it all together to form a dough.
2. Cut the dough with a pastry scraper, using a downward cutting action, then turn the dough and repeat in the opposite direction. The dough should now come together to form a soft ball. Score a cross in the top to prevent shrinkage, wrap, and refrigerate for 15-20mins.
3. Soften the remaining butter by pounding it between two sheets of parchment paper with a rolling pin. Then, still between the papers, roll it into a 4in square. The butter must be the same consistency as the dough or they will not roll out the same amount and the layers will not be even. If the butter is too soft, it will squeeze out of the sides. Too hard and it will break through the dough and disturb the layers.
4. Put the pastry on a well-floured surface. Roll it out to form an X (more like a square whose corners are swelled than lines), leaving the center slightly thicker than the arms. Place the butter in the center of the X and fold over each of the arms to make a parcel. Turn the dough so that it looks like a book with the hinge side to the left. Tap and roll out the dough to form a 6x18in rectangle. Make this as neat as possible, squaring off the corners- otherwise, every time you fold, the edges will become less neat and the layers will not be even.
5. Fold the dough like a letter, the top third down and the bottom third up, to form a square, brushing off any excess flour between the layers. Turn the dough 90 degrees to bring the hinge side to your left and press the seam sides down with the rolling pin to seal them. Re-roll and fold as before to complete two turns and mark the dough by gently pressing into the corner with your fingertip for each turn - this will remind you where you're up to. Wrap the dough in plastic wrap and chill again for at least 30mins.
6. Re-roll and fold twice more and then chill, and then again to complete six turns. If it is a very hot day, you may need to chill for 30mins between each turn, rather than doing a double turn as described above. The pastry should now be an even yellow and is ready to use - if it looks a little streaky, roll and fold once more. The aim is to ensure that the butter is evenly distributed throughout so that the pastry rised and puffs up evenly when baked. Refrigerate until needed.
You need enough dough for this that it can make a (roughly) 10in square 1/8in thick.
The lines on the pastry shown are from being folded in thirds for freezing. Pay no attention to them.