Cook linguine according to package directions. Reserve about 1 cup of pasta water before draining.
While pasta is cooking, melt butter in a large skillet over medium heat.
Add minced garlic and red pepper flakes (if using) to the skillet and cook until fragrant, about 1 minute, being careful not to burn the garlic.
Add shrimp to the skillet and season with salt and pepper. Cook until pink and opaque, about 2-3 minutes per side.
Pour in heavy cream and bring to a simmer. Stir in grated Parmesan cheese until melted and the sauce is slightly thickened.
Add the drained linguine to the skillet with the shrimp and sauce. Toss to combine, adding a splash of reserved pasta water if needed to reach desired consistency.
Stir in fresh chopped parsley. Taste and adjust seasoning if necessary.
Serve immediately.
Notes
For an extra kick, add a pinch of cayenne pepper along with the red pepper flakes. You can also add a squeeze of lemon juice at the end for brightness.