Step 1

Combine 3/4 cup warm water (105°-115°F), sugar, and yeast in a large bowl; let sit until spongy, 4-5 minutes. Mix in 1 1/2 tablespoons oil and 1 teaspoon salt. Stir in 2 1/4 cups flour. Turn out onto a work surface; knead until smooth and elastic, adding more flour if sticking, about 6 minutes. Grease a large bowl with 1 tablespoon oil. Add dough, cover bowl with plastic; let rise until doubled, about 1 1/2 hours.

Step 2

Meanwhile, position one rack in top third of oven and another in bottom third; place a pizza stone on top rack and preheat oven to 500°F. Scatter tomatoes on a large rimmed baking sheet. Add 1 tablespoon oil, toss, and season with salt and pepper. Place on lower rack; roast until skins split, 10-12 minutes. Let cool on rack. Continue heating pizza stone for 45 more minutes.

Step 3

Sprinkle a pizza peel or rimless baking sheet with semolina. Divide dough in half; roll or stretch each into a 13x9" rectangle. Cover with kitchen towels; let stand for 15 minutes. Transfer 1 rectangle to prepared pizza peel. Brush with 2 tablespoons oil, sprinkle with half of the Parmesan, then mozzarella, and top with half of the tomatoes. Season with salt and pepper.

Step 4

Set front of peel at far edge of stone; gently jiggle peel side to side, sliding pizza onto stone as you remove peel. Bake until crust is browned and crisp, 9-10 minutes. Using peel, transfer pizza to work surface. Garnish with basil. Slice and Serve.

Step 5

Repeat to make second pizza.