Heat olive oil in a 5-quart Dutch oven over medium heat. Add garlic and red pepper and stir for 30 seconds without browning the garlic.
Add tomatoes and salt and cook for 5 minutes, stirring and crushing some softened tomatoes with a wooden spoon.
Add fusilli and 3 cups water. Bring to a boil, then reduce to a steady uncovered simmer and cook for 12 to 15 minutes, stirring from the bottom every 2 minutes.
Add the remaining 1/2 cup water a few tablespoons at a time only if the pot gets dry before the pasta is tender. Simmer until the sauce clings to the twists rather than pooling like soup.
Remove from the heat and fold in basil and Parmesan. Rest for 2 minutes, loosen with any remaining measured water if needed and divide among 4 bowls.