1 (1/4-ounce) package active dry yeast (2 1/4 teaspoon)
1 3/4 cups unbleached all-purpose flour, divided, plus more for dusting
3/4 cup warm water, divided
1 teaspoon salt
1/2 tablespoon olive oil
1 (14-to 15-ounces) can whole tomatoes in juice
2 large garlic cloves, smashed
2 tablespoons olive oil
4 basil leaves plus more for sprinkling
1 plus more for sprinkling
1/4 teaspoon sugar
6 ounces fresh mozzarella, cut into 1/4-inch-thick slices
Stir together yeast, 1 tablespoon flour, and 1/4 cup warm water in a large bowl and let stand until surface appears creamy, about 5 minutes.
Add 1 1/4 cups flour, remaining 1/2 cup water, salt, and oil and stir until smooth. Stir in enough flour (1/4 to 1/3 cup) for dough to begin to pull away from side of bowl. (Dough will be slightly wet.) Knead on a floured surface, lightly re-flouring when dough becomes too sticky, until smooth, soft, and elastic, about 8 minutes. Form into a ball, put in a bowl, and dust with flour. Cover with plastic wrap or a kitchen towel (not terry cloth) and let rise in a draft-free place at warm room temperature until doubled, about 1 1/4 hours.
Make tomato sauce while dough rises. Pulse tomatoes with juice in a blender briefly to make a chunky puree. Cook garlic in oil in a small heavy saucepan over medium-low heat until fragrant and pale golden, about 2 minutes. Add tomato purée, basil, sugar, and 1/8 teaspoon salt and simmer, uncovered, stirring occasionally, until thickened and reduced to about 3/4 cup, about 40 minutes. Season with salt and cool.
At least 45 minutes before baking pizza, put stone on oven rack in lower third of electric oven (or on floor of gas oven) and preheat oven to 500°F.
Do not punch down. Dust dough with flour, then transfer to a parchment-lined pizza peel or large baking sheet. Pat out dough evenly with your fingers and stretch into a 14-inch round, re-flouring fingers if necessary.
Spread sauce over dough, leaving a 1-inch border (there may be some sauce left over). Arrange cheese on top, leaving a 2- to 3-inch border.
Slide pizza on parchment onto pizza stone. Bake until dough is crisp and browned and cheese is golden and bubbling in spots, 13 to 16 minutes.
Using peel or baking sheet, transfer pizza to a cutting board. Cool 5 minutes. Sprinkle with torn basil leaves before slicing.