1Bring a large pot of salted water to a boil and cook the spaghetti until al dente, about 9 minutes. Reserve 1 cup of pasta water, then drain.
2While the pasta cooks, warm the extra virgin olive oil in a large skillet over medium heat. Add the minced garlic and cook for 30 seconds until fragrant—do not brown it.
3Add the tomato chunks to the skillet and cook for 2–3 minutes, stirring gently, just until they begin to soften and release their juices. The tomatoes should stay mostly whole.
4Add the hot drained pasta directly to the skillet and toss gently with the tomatoes and oil. Add pasta water a splash at a time to create a light, silky sauce—you'll likely use 1/4 to 1/2 cup.
5Remove from heat. Add the torn mozzarella and most of the torn basil, tossing gently until the cheese softens slightly from the residual heat.
6Squeeze the lemon over the top, then taste and season with salt and black pepper. Divide among bowls, top with remaining basil, and serve immediately.