Preheat oven to 375 degrees. Place grape tomatoes on a baking sheet lined with parchment paper. Bake until tomatoes are blistered, about 15 minutes.
While the tomatoes roast, bring 4 quarts of water and 1 tablespoon salt to a boil. Add the pasta and cook until the pasta is al dente, about 10 to 12 minutes.
When the tomatoes are done roasting, combine tomatoes, olive oil, vinegar, and garlic. Season to taste with salt, pepper, and cayenne pepper (if using). Toss until evenly coated and let marinate at room temperature.
Drain the pasta but do not rinse. Add the tomato mixture and toss together. Add the mozzarella and the finely shredded basil, and toss. Season to taste with salt and pepper. Garnish with the basil sprigs and serve.
Notes
Use firm garlic cloves that do not show any signs of green sprouts. The sprouts will impart a sharp flavor if included in this dish.