Cook pasta according to package directions. Drain, reserving about 1/2 cup of pasta water.
While pasta is cooking, heat olive oil in a large skillet over medium heat. Add minced garlic and cook until fragrant, about 1 minute.
Add shrimp to the skillet and cook for 2-3 minutes per side, until pink and cooked through. Remove shrimp from skillet and set aside.
Pour heavy cream into the skillet and bring to a simmer. Stir in shredded mozzarella cheese, grated Parmesan cheese, and red pepper flakes (if using). Cook, stirring, until cheese is melted and sauce is smooth.
Return the cooked shrimp to the skillet. Add the drained pasta and toss to combine. If the sauce is too thick, add a little reserved pasta water until desired consistency is reached.
Season with salt and black pepper to taste. Stir in chopped fresh parsley.
Serve immediately.
Notes
This recipe can be customized with your favorite vegetables, such as spinach or cherry tomatoes.