Begin by cooking the linguine according to package instructions until al dente. Reserve 1/2 cup of pasta water before draining and set aside.
In a large skillet over medium heat, melt the butter and olive oil together. Once melted, add in the minced garlic and red pepper flakes, sautéing until fragrant, about 1 minute.
Add the shrimp to the skillet, seasoning them with salt and pepper. Cook for about 2-3 minutes on each side, or until the shrimp turn pink and opaque.
Stir in the lemon zest and fresh lemon juice, mixing well to combine and allow the flavors to meld.
Add the cooked linguine to the skillet, tossing to coat the pasta in the garlic shrimp sauce. If the mixture appears too dry, gradually add in reserved pasta water until you reach the desired consistency.
Finish with chopped parsley, stirring to incorporate. Adjust seasoning with more salt and pepper if necessary.
Serve immediately, topped with freshly grated Parmesan cheese if desired.