Begin by bringing a large pot of salted water to a boil. Add the linguine and cook according to package instructions, typically about 8-10 minutes, until al dente. Reserve 1 cup of pasta water, then drain and set aside.
In a large skillet over medium heat, melt the butter and olive oil together. Add the minced garlic and red pepper flakes, sautéing for about 1-2 minutes until fragrant.
Incorporate the shrimp into the skillet, seasoning with salt and black pepper. Cook for about 3-4 minutes, flipping halfway through, until the shrimp are pink and opaque.
Once the shrimp are cooked, add the drained linguine to the skillet, tossing gently to combine. Pour in the reserved pasta water (start with half and add more if needed) along with the lemon zest and lemon juice, stirring everything together for 1-2 minutes until heated through and the sauce has coated the pasta.
Remove from heat and stir in the chopped parsley. Taste and adjust seasoning if needed.
Plate the pasta by twirling it onto a plate or serving dish. If desired, sprinkle grated Parmesan cheese over the top for added flavor.
Notes
Adjust the red pepper flakes to your spice preference.