Baked Tomato Basil Butter Pasta

Name: Baked Tomato Basil Butter Pasta
Ingredients: 6 garlic cloves; 2 lb. (1 kg) cherry tomatoes; 1 Tbs. extra-virgin olive oil; 1 tsp. sugar; Kosher salt; 1/4 tsp. red pepper flakes, plus more for serving; 8 oz. (250 g) pasta (any short noodle); 3 fresh basil sprigs; 1 1/4 cups (10 fl. oz./310 ml) hot water, plus more as needed (as hot as your sink will go; doesn’t need to be boiling); 8 Tbs. (1 stick) (4 oz./125 g) unsalted butter; 1/2 cup (2 oz./60 g) grated Parmesan cheese, plus more for serving