I'm going to turn a bowl using my lathe equipped with an adjustable chuck, as well as the table saw. For that I will use these pieces of olive wood obtained from Mediterranean olive trees, which are pruned yearly.

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Video:

Step 1: Glue and Cut

First I'll glue the wood like this. Once it's dry, I'll cut it with the table saw to obtain the desired thickness and end grain, which gives it a more ornate look. I apply glue again making sure the cut lines in the wood blocks don't line up.

Then I'll mark the outer diameter to cut with the band saw.

Step 2: Turning

Using the same center, I will mark the diameter of the faceplate to place it in the center. I screw it in and put it in the lathe to start the machining process.

Since the bowl is quite wide, I will use the slowest lathe speed and a roughing gouge. Olive wood is less than ideal for turning. It is quite hard and its grain swirls, and since we're turning against the end grain, this is made even more difficult. Still, little by little I turn the bowl into shape.

I'll mark the center with a small protrusion that I will later use to hold the bowl on the table saw.

Step 3: Machine the Interior

I'll also take the chance to sand the bowl's exterior. Before removing it, I'll mark the center of the bowl on the bottom with the tailstock.

I've marked a square on my table saw to help me place the bowl and I've prepared this template to machine the interior. We must make sure the center is marked properly so that the disc doesn't cut through the bowl at any point. It could be dangerous if that happens.
I move the disc up gradually, in 3mm increments, making each cycle slowly, every so often I will detach the template to see if it looks good and wipe off the sawdust.

Step 4:

Now I'll attach the adjustable chuck on the lathe and put the bowl on it. To center it, I'll put the tailstock in the center of the bowl again.

Using a good metal chuck, we could machine the bowl on the lathe. I thought about making one, but I believe it's too complex to make. Besides, it would be very dangerous if it came loose. That's why I've decided to buy a chuck which I'm going to adapt to my lathe's shaft.

I tighten the silent blocks gradually and make sure the bowl is firmly held.

I finish machining the bottom part of the bowl, making a little rebate to avoid unsteadiness when putting it on a table. I will also fill in the cracks on the exterior with a little red epoxy and take advantage of the rotation to do a little more sanding. I'll fill the cracks on the inside with black epoxy.
Some of you have asked me about the toxicity of epoxy. Once it is hardened it is safe, it's no different than a piece of plastic. Even metal food cans contain an epoxy layer inside... Anyway, I prefer to use a small amount, in this case there are only a few small cracks outside.

I also apply a little mineral oil. The end grain on olive wood never ceases to amaze me. It's hard to work with, but the result more than makes up for it!