How to Make It
In a large bowl, stir together warm water with yeast and sugar and let stand until foamy, about 5 minutes.
Stir 3/4 cup flour and 3 tablespoons olive oil into yeast mixture. Let stand until small bubbles appear, about 20 minutes.
Brush a large bowl with 1 tablespoon olive oil. Stir remaining 1 cup and 2 tablespoons flour and 3/4 teaspoon salt into dough. On a lightly floured work surface, knead the dough until it comes together in a uniform ball. Transfer to prepared bowl, cover with plastic wrap, and let stand until the dough has doubled in size, about 1 hour and 15 minutes.
Meanwhile, in a medium saucepan, heat 1 tablespoon olive oil. Add garlic and cook over moderate heat, stirring, until garlic begins to turn light golden, about 30 seconds. Stir in crushed tomatoes and bring to a simmer. Remove from heat, season with salt and pepper, and let cool.
Brush a 13-by-18-inch rimmed baking sheet with 1 tablespoon olive oil and press dough into pan. Using fingers, dimple the dough all over and drizzle with the remaining 1 tablespoon olive oil. Let dough rise until puffed, about 30 minutes.
Preheat oven to 450°. Spread 6 tablespoons sauce over dough, leaving a 1/2-inch border; reserve remaining sauce for another use. Tear stracciatella into pieces and scatter over pizza. Bake until crust is golden and the cheese is lightly browned, about 25 minutes. Scatter basil leaves over pizza and serve.