Preheat the oven to 450 degrees F

To make the crust: Stir the water, 1 tablespoon of the sugar, and the yeast together in a small bowl. Let stand until foamy, about 10 minutes. Meanwhile, heat the milk in a small saucepan. Remove from heat, add the butter, and stir until melted.

In a large bowl, stir together the flour, cornmeal, remaining sugar, egg, milk mixture, yeast mixture, and salt until a soft dough forms. Turn dough out onto a floured surface and knead until smooth, adding flour as needed if dough is sticky, about 10 minutes. Clean the bowl and coat it generously with olive oil. Form the dough into a ball, put it in the bowl and cover with a kitchen towel. Let rise in a warm place until doubled in size, about 1 hour.

Punch the dough down and let rest for 10 minutes.

Cut the mozzarella into sticks about 3 by 3/4 by 3/4-inches. Sprinkle a large baking sheet with cornmeal. Place the dough on the baking sheet and stretch it into a 15-inch circle.

Arrange the mozzarella sticks around the dough about 1-inch in from the edge, then roll the dough over the cheese to form the stuffed rim.

To make the topping: Stir the sugar into the marinara sauce and spread onto the pizza dough. Scatter with the stewed tomatoes, then the mozzarella. Add the onions, mushrooms, and pepperoni. Sprinkle with basil and oregano.

Bake until crust is golden brown, 15 to 20 minutes. Cut into wedges and serve immediately.