In a large pot or deep skillet, melt the butter over medium heat. Add the minced garlic and red pepper flakes, sautéing for about 1 minute until fragrant.
Add the shrimp to the pot and cook for 2-3 minutes, or until they turn pink and opaque. Remove the shrimp from the pot and set aside.
In the same pot, add the chicken broth, heavy cream, lemon zest, and lemon juice. Bring to a simmer.
Add the linguine or spaghetti to the pot, stirring to combine. Cook according to package instructions, usually about 8-10 minutes, until the pasta is al dente. Stir occasionally to prevent sticking.
Once the pasta is cooked, return the shrimp to the pot. Season with salt and pepper to taste. Stir in the chopped parsley and grated Parmesan cheese until well combined.
Serve immediately, garnished with additional parsley and Parmesan if desired.