Boil a large pot of salted water and cook pasta according to package directions minus 1 minute. Reserve 1 cup pasta water before draining.
Heat olive oil in a large skillet over medium heat. Add minced garlic and cook for 1 minute, stirring constantly until fragrant but not browned.
Add crushed tomatoes, salt, pepper, and red pepper flakes. Simmer for 5-7 minutes, stirring occasionally.
Lower heat and stir in heavy cream until well combined. The sauce should turn a peachy color.
Toss drained pasta into the skillet with the sauce. Add pasta water as needed to reach desired consistency.
Remove from heat and stir in fresh basil and half the Parmesan. Serve immediately with remaining cheese on top.
