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Combine warm water, sugar, and yeast in a large bowl. Stir gently and let sit 5-10 minutes until foamy.
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Add flour, salt, and olive oil. Stir until a shaggy ball forms. Turn onto a floured surface and knead 5 minutes until smooth and slightly tacky.
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Shape into a ball, place in the bowl with a drizzle of olive oil. Cover with a towel and let rise 1 hour until doubled.
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While dough rises, make the sauce: heat olive oil, cook garlic 30 seconds, add crushed tomatoes, oregano, basil, sugar, salt, and pepper. Simmer 15-20 minutes.
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Preheat oven to 475°F with a baking sheet or pizza stone inside.
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Punch down dough and divide into 4 equal pieces. Roll or stretch each into an 8-10 inch circle on parchment paper.
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Spread 3-4 tablespoons sauce on each, leaving a half-inch border. Add cheese and toppings.
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Slide pizza on parchment onto hot baking sheet. Bake 12-15 minutes until crust is golden and cheese is bubbly with brown spots.
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Let cool 2-3 minutes on a cutting board before slicing and serving.