Cook the pasta in a large pot of salted boiling water according to package instructions until al dente. Reserve 1 cup pasta water, then drain and set aside.
Heat olive oil and 2 tablespoons butter in a large skillet over medium-high heat until butter melts and bubbles.
Add minced garlic and red pepper flakes to the skillet and sauté about 1 minute until fragrant, avoiding burning the garlic.
Place shrimp in a single layer in the skillet and cook 2-3 minutes on each side until pink and cooked through. Remove shrimp and set aside.
Pour white wine into the skillet, bring to simmer, and scrape up brown bits. Reduce for 2-3 minutes.
Stir in lemon juice and zest, then whisk in the remaining 2 tablespoons butter until melted and sauce combines.
Return shrimp to the skillet and add the drained pasta. Toss to coat, adding reserved pasta water gradually if sauce is too dry.
Season with salt and black pepper to taste, sprinkle chopped parsley, and toss gently.
Remove from heat and serve immediately topped with grated Parmesan cheese.