Christina's Stuffed-Crust Pepperoni and Mushroom Pizza

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Crust:

1/4 cup warm water

4 tablespoons sugar

1 package dry yeast

3/4 cup milk 

4 tablespoons unsalted butter

2 1/2 cups all-purpose flour, plus more for kneading

3 tablespoons cornmeal, plus more for the pan

1 egg, beaten

1 teaspoon salt

8 ounces mozzarella

Olive oil, for coating bowl

Topping:

1 tablespoon sugar

3/4 cup prepared marinara sauce

1/2 cup canned stewed tomatoes, strained and coarsely chopped

1 1/2 cups grated mozzarella

1 medium onion, finely chopped

1/2 cup sliced mushrooms

1/4 pound sliced pepperoni

1 teaspoon dried basil

1 teaspoon dried oregano