Put the starter, flour, and salt into the bowl of a stand mixer. If you are using a very healthy starter, and not Discard, you can omit the yeast.
Put the smaller amount of water in the bowl and stir until all the water is absorbed and the dough has started forming a ball. Add the oil, If you don't have a ball, continue adding water a teaspoon at a time until the ball forms and there is very little residual flour on the sides of the bowl.
Put the machine on 2 and knead for 7 minutes.
Meanwhile, prepare a bowl by putting some oil in it. Remove the dough from the machine and put it in the oiled bowl. Cover it and keep it in a warm place until it doubles in bulk, about 90 minutes.
Preheat the oven to 500 °F (260 °C). Break off a piece of parchment paper large enough to fit your pizza peel or baking sheet. If you have not already done so, put your pizza stone in the oven. Do this about 20 minutes before the dough has doubled.
Make the Sauce
When the dough has risen enough make the sauce by combining the sauce ingredients in a small pot. Taste for seasoning and let it just come to a boil then turn off the heat and set it aside.
Make the Calzones
Form dough into two balls. Roll one of the balls into a circle about 12 inches in diameter.
Spread some of the sauce in the middle of the dough, leaving about 2 inches uncovered on the edge. Put the filling in the center. Pull the sides up and press them together, then bring up the ends and press them into the sides to seal them.
Do this for the other ball.
Before putting the calzones in the oven, mix the egg with the water and paint the calzones. Sprinkle them with the sesame seeds, the black for meat, the plain for vegetables.
Bake the calzones for 20 minutes or until the crust has deeply browned. Let them sit for about 10 minutes before cutting into them.
Put any remaining sauce in a bowl for dipping and serve. Enjoy!
Scan for full nutrition info and step-by-step photos.