1 1/2 pounds plum tomatoes, peeled and halved lengthwise $
3 tablespoons extra-virgin olive oil, divided $
2 garlic cloves, minced
2 tablespoons plus 1/2 teaspoon fine sea salt, divided $
1/4 teaspoon crushed red pepper
6 quarts water $
12 ounces uncooked spaghetti $
1/4 cup minced fresh basil
6 tablespoons grated fresh Parmigiano-Reggiano cheese