Spaghetti with Tomato Saute

Name: Spaghetti with Tomato Saute
Ingredients: 3 tablespoons extra-virgin olive oil, plus more for drizzling; 3 pints red, orange, and yellow pear or cherry tomatoes (about 2 pounds), halved if large; plus a few more, still on the vine (optional); Kosher salt; 2 cloves garlic, minced; Large pinch of red-pepper flakes, plus more for serving; 12 ounces spaghetti or bucatini; 2 ounces Parmigiano-Reggiano, finely grated (½ cup); ½ cup fresh ricotta cheese; Small fresh basil leaves, for serving