In a large mixing bowl, combine 1.5 cups warm tap water and 1.5 teaspoons granulated sugar; stir until the sugar dissolves. Sprinkle 1.5 teaspoons active dry yeast over the surface, stir a few times, and let sit until foamy (about 5 minutes).
Add 2 cups all-purpose flour to the bowl and mix with a wooden spoon until combined. Stir in 1 tablespoon vegetable or canola oil.
Add 1 more cup of flour (the third cup) and stir until incorporated.
Turn the dough onto a lightly floured surface and knead while gradually incorporating the remaining 1 cup of flour. Knead until the dough is smooth and no longer sticky.
Place the dough into a large bowl that has been lightly greased with oil, turning the dough once so its top is lightly oiled. Cover with a kitchen towel and place in a warm, draft-free spot until doubled in size (about 1 hour).
While the dough rises, lightly grease two pizza pans with oil for greasing pans and sprinkle the pans with cornmeal for dusting pans.
After the dough has doubled, punch it down and transfer it to a floured surface. Smooth it into a ball and divide it into two equal pieces.
Roll or stretch one piece into a circle roughly the size of your pizza pan. Place it on one prepared pan and stretch the edges as needed to fit.
Preheat the oven to 420°F.
Place the prepared pan with the dough in the preheated oven and par-bake the crust for 7 minutes.
Remove the par-baked crust from the oven. Brush the crust edges with 1 tablespoon melted butter and sprinkle 1 tablespoon yellow cornmeal evenly over the crust edges.
Spread 1 cup pizza sauce over the dough, leaving a small border at the edges. Arrange approximately half of the pepperoni slices, half of the 1/2 cup chopped green peppers, half of the 1/2 cup chopped yellow onion, half of the 1/2 cup sliced mushrooms, and half of the 2 cups shredded mozzarella cheese evenly over the sauce.
Bake the assembled pizza at 420°F for 12 to 15 minutes, or until the cheese is melted and bubbling and the crust edges are golden.
Repeat steps 8–13 with the second piece of dough, using the remaining prepared pan, 1 cup pizza sauce, the remaining toppings (pepperoni, peppers, onion, mushrooms, and cheese), 1 tablespoon melted butter, and 1 tablespoon yellow cornmeal.