Make the dough: In a bowl, mix warm water and sugar. Sprinkle in the yeast. Let it sit for 5 minutes until foamy. Add flour, salt, and olive oil. Mix and knead for 8–10 minutes until smooth. Cover and let it rise in a warm spot for about 1 hour or until doubled.
Prep toppings: While dough rises, wash and slice all vegetables. Grate the cheese if needed.
Shape the dough: Punch down the risen dough. Divide it into two equal balls. Roll each out on a lightly floured surface to about 10–12 inches wide.
Assemble the pizza:: Preheat oven to 475°F (245°C). Place dough on a baking sheet or pizza stone lined with parchment. Spread pizza sauce thinly. Sprinkle mozzarella. Add veggies evenly. Sprinkle oregano on top. Lightly brush the crust edges with olive oil.
Bake: Bake each pizza for 12–15 minutes until the crust is golden and the cheese bubbles. Slice and serve hot!