Let dough come to room temperature, at least 30 minutes. Place a rack in lower third of oven; preheat to 425°F (218°C).
Drain tomatoes in a fine-mesh sieve set over a large bowl. Using your hands, crush tomatoes as finely as you can. Let sit in sieve to continue draining, about 2 minutes. Discard or reserve liquid for another use.
Place tomatoes in the bowl. Add half of the garlic, 1/3 of the oil, and salt and mix to combine.
Generously grease a baking sheet with oil. Gently punch down dough and transfer to prepared tray. Using your fingers and sides of your palms, gently stretch dough to fill the whole tray. If dough springs back, cover with plastic wrap and let dough rest at room temperature for 10 minutes. Top dough with cheese and dollop with sauce, leaving a 1/2" border on all sides. Add any toppings of choice if using.
Bake pizza until cheese is bubbling and crust is deeply golden, 20 to 25 minutes.
In a small bowl, mix basil and remaining garlic and remainingoil; season with salt. Sprinkle basil leaves over pizza.