Cook pasta in salted water according to package directions until al dente. Drain and set aside.
While pasta cooks, heat olive oil in a large skillet over medium-high heat. Add shrimp, season with salt and pepper, and cook for 1-2 minutes per side until pink and cooked through. Remove from skillet.
In the same skillet, melt butter over medium heat. Add garlic and red pepper flakes. Cook until fragrant, about 1 minute.
Return pasta and shrimp to the skillet. Add lemon juice, zest, and Parmesan cheese. Toss everything together until well coated in the garlic butter sauce.
Top with chopped parsley and serve hot.