Chef John's Ham and Cheese Pockets

Preheat the oven to its highest temperature setting, 500 degrees F (260 degrees C). Next, cover a baking sheet with parchment paper to prevent sticking.

Divide the dough into four equal parts; shape each portion into a spherical form. On a surface lightly dusted with flour, flatten each dough sphere into a flat disc and roll it out to form an 8- or 9-inch round circle.

Place two prosciutto slices on one half of each dough circle, leaving a 1-inch border around the edges. Spread ricotta cheese over the prosciutto, then season with a pinch of salt, pepper, and cayenne pepper. Add chopped ham, mozzarella slices, and a drizzle of olive oil on top.

Dampen the edge of each dough circle with a small amount of water using your fingertip. Fold the empty half of the dough over the filling and seal the edges by pressing them together firmly. Crimp the edges to ensure a tight seal.

Sprinkle a layer of cornmeal onto the prepared baking sheet. Carefully place the calzones on the baking sheet, making sure not to touch the edges of the cornmeal. Use a knife to make several small slits in the top crust, allowing steam to escape during baking.

Mix egg and water together to create an egg wash. Brush the calzones with the egg wash, then sprinkle grated Parmigiano-Reggiano cheese on top. Remove any excess cornmeal and cheese from around the calzones to prevent smoke during baking.

Bake the calzones in the preheated oven until they are golden brown, approximately 15 minutes. Allow them to cool for 15 minutes before serving. Serve with heated marinara sauce on the side for dipping.