Cut the cherry tomatoes in 1/2; remove the cores of the large tomatoes and cut into pieces about 1/2-inch square. Put the tomatoes in a glass, ceramic or stainless mixing bowl.
Add salt, about 1/2 teaspoon, to taste and toss. Add the garlic, 1/2 of the basil, the capers, and red pepper flakes if using; add the olive oil and toss. Cover the bowl with plastic wrap and refrigerate for 1 hour.
Bring a large pot of water to a boil. Add salt to the water and cook the pasta until al dente. Strain the pasta and add to the mixing bowl with the tomatoes. Add the remaining basil, some Parmigiano and toss.