Bring a large pot of salted water to a boil and cook the linguine until just al dente. Reserve 1/2 cup of the pasta water, then drain the pasta.
While the pasta cooks, pat the shrimp dry and season lightly with salt and pepper.
Heat the olive oil and 2 tablespoons of butter in a large skillet over medium heat. Add the minced garlic and red pepper flakes and cook for 30 seconds until fragrant.
Add the shrimp in a single layer. Cook for 2 minutes, then flip and cook 1 minute more until pink and opaque.
Lower the heat and add the remaining 2 tablespoons of butter, lemon juice, and a splash of the reserved pasta water. Stir until the butter melts and the sauce looks glossy.
Add the drained linguine to the skillet along with the chopped parsley. Toss everything together, adding more pasta water if needed to loosen the sauce. Taste and adjust salt and pepper.
Remove from heat and serve right away with grated Parmesan on top.