Cook the linguine or spaghetti according to package instructions until al dente. Reserve 1 cup of pasta water, then drain and set aside.
In a large skillet over medium heat, melt the butter. Add minced garlic and sauté for about 1-2 minutes until fragrant. Be careful not to burn it.
Add the shrimp to the skillet and season with salt, pepper, and red pepper flakes. Cook for about 2-3 minutes on each side until the shrimp turns pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, pour in the heavy cream and bring to a simmer. Gradually whisk in the Parmesan cheese until melted and the sauce is smooth.
Add the cooked pasta to the skillet and toss to coat in the sauce, adding reserved pasta water as needed to achieve desired sauce consistency.
Stir in the lemon zest and the cooked shrimp until everything is heated through. Adjust seasoning with salt and pepper as necessary.
Garnish with fresh parsley before serving.
Notes
Adjust red pepper flakes to taste for desired spiciness.