Combine oil, garlic, and 3/4 tsp. salt in a large bowl. Chop 1 cup of the tomatoes and add to bowl. Cut remaining tomatoes in half and stir into mixture; let stand about 30 minutes, stirring occasionally.
Meanwhile, cook pasta as package directs in a large pot of salted boiling water.
Drain pasta, saving 1 cup water. Toss pasta with tomato mixture, then with cheese and all but 1 tbsp. basil. Mix in a little pasta water if needed for a looser texture. Sprinkle remaining basil on top and season with salt.