Stir the active dry yeast and sugar into warm water (105–110°F / 40–43°C). Let stand for 5 minutes until foamy.
Add the flour, salt, and olive oil. Knead for 6–8 minutes until smooth and elastic.
Transfer the dough to a lightly oiled bowl, cover, and let rise until puffy, 45–60 minutes.
Heat the oven to 500°F (260°C) with a pizza stone or inverted heavy baking sheet inside for at least 30 minutes.
Mix crushed tomatoes with garlic, oregano, olive oil, and salt. Divide the dough in half and stretch each piece into a 12-inch round; spread a thin layer of sauce over each.
Add mozzarella and desired cooked toppings. Bake one pizza at a time for 8–12 minutes, until the crust is browned and the cheese bubbles.
Rest each pizza for 2 minutes, add fresh basil, and slice.