In a large bowl, combine 1½ cups warm water, 2 tablespoons granulated sugar, and 1 tablespoon active dry yeast; stir and let sit 5 minutes until foamy.
Add 3½ cups all-purpose flour and 1 teaspoon salt to the yeast mixture; mix until a smooth dough forms using a stand mixer with a dough hook or by hand.
Let the dough rise for 10 minutes in a warm spot.
Divide or portion the dough to the desired pizza size (the author divided it in half to make two pizzas); let portions rest 10 minutes, then roll out on a lightly floured surface.
Place the rolled dough on a baking sheet or preheated pizza stone. Spread the 14-ounce jar of pizza sauce evenly, leaving about a 1-inch border.
Sprinkle 2 cups shredded mozzarella evenly over the sauce, then add pepperoni, mushrooms, olives, and green peppers as desired.
Bake in a 400°F (204°C) oven for 15–20 minutes, until the crust is golden and the cheese is bubbly.