Prepare the pasta by boiling salted water in a large pot. Cook the fettuccine or linguine according to package instructions until al dente. Drain and set aside.
In a large skillet over medium heat, melt 2 tablespoons of butter. Add the shrimp, season with salt and pepper, and sauté until pink and opaque (about 2-3 minutes per side). Remove from skillet and set aside.
In the same skillet, add another tablespoon of butter and minced garlic. Sauté for about one minute until fragrant. Pour in chicken broth and heavy cream; bring to a simmer.
Stir in grated Parmesan cheese and red pepper flakes. Add the cooked shrimp back to the skillet, tossing gently to combine.
Add the drained pasta to the sauce mixture, tossing until well-coated.
Serve hot, garnished with extra Parmesan if desired.
