Ingredients for dough: 

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

Ingredients for topping:
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
1/4 teaspoon sugar
6 ounces fresh mozzarella, cut into 1/4-inch-thick slices

Preparation:
Make dough - stir yeast together, 1 tablespoon flour, and 1/4 cup of warm water in a large bowl. Let stand until surface appears creamy, about 5 minutes. Add 1 1/4 cups of flour and 1/2 cup of water, salt and oil, stir until smooth. Add flour until dough pulls away from sides.Knead on a floured surface, lightly reflouring 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 purée. 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.