For the dough:

1. In a small bowl, combine the yeast and sugar with 1/2 cup of the warm water and set aside until foamy, about 10 minutes. In the bowl of a heavy-duty mixer fitted with a dough hook, combine flour, semolina, cornmeal, salt, pepper and garlic. Pour in the olive oil and mix until combined. Add the rest of the water and scrape in the yeast mixture. Knead the dough for approximately 10 minutes, or until it is elastic and forms a ball, adding additional flour if needed to keep the dough from sticking. Oil a large bowl and turn the dough into the bowl, coating it lightly with the oil. Cover with plastic and allow to rise in a warm draft-free place until it has doubled in size, approximately 1 hour. While the dough is rising, prepare the sauce and toppings.
2. Punch the dough down and turn it out onto a lightly floured work surface. Allow the dough to rest for 10 minutes. Divide the dough in quarters. One quarter portion of the pizza dough can be made into a free-form crust and cooked on a baking sheet or lightly oiled pizza screen, or directly in the oven on a pizza stone.
3. Roll one portion of dough out on a lightly floured surface and transfer to a pizza screen or a peel that has been lightly dusted with cornmeal if using a pizza stone.

For the sauce:

1. Heat a tablespoon of the olive oil in a skillet over medium-high heat. When hot, add the tomatillos, cilantro, oregano, garlic and onion and sauté for 5 minutes, stirring frequently.
2. Place the mixture in a blender or food processor. Purée, then add the egg yolks, Parmesan cheese and remaining olive oil. Season with salt and pepper and set aside.

Mushrooms and chorizo (if using):

1. Heat the olive oil in a skillet over medium heat. Add the mushrooms, onions and garlic and sauté for 2 minutes over medium heat. Cover the pan, lower the heat and allow the mixture to cook for 10 minutes, stirring occasionally. Uncover the pan, raise the heat to high, deglaze with the sherry and reduce until almost no liquid remains. Season with salt and pepper to taste.
2. Sauté the sausage in a medium skilled over medium heat, breaking it into small pieces, until completely cooked. Transfer to paper towels to remove excess fat.

Assembling and baking the pizzas:

1. Preheat the oven to 500°F. If using a pizza stone begin preheating the oven at least 30 minutes before you plan to bake the pizzas.

2. Paint the dough with sauce and sprinkle with additional Parmesan cheese, if desired. Spread 1/4 of the mushroom mixture on top of the sauce and sprinkle with the cooked sausage (if using). Then, arrange slices of the bell peppers, green chile, cheese and tomato over the mushrooms. Top with the fresh cilantro leaves.

3. Bake the pizza for 12 to 15 minutes. Repeat with the remaining dough and toppings. Serve.