Cook the pasta: Bring a large pot of salted water to a boil. Cook the fettuccine until al dente according to package directions. Reserve 1 cup of pasta water, then drain.
Cook the shrimp: In a large skillet, heat 2 tbsp butter and olive oil over medium-high heat. Season shrimp with salt and pepper. Add shrimp to skillet and cook 1–2 minutes per side, until pink and opaque. Remove shrimp and set aside.
Make the garlic butter sauce: In the same skillet, melt the remaining 2 tbsp butter. Add minced garlic and sauté for 1 minute until fragrant. Pour in white wine (or broth), scraping up browned bits from the pan. Simmer for 2–3 minutes until slightly reduced.
Combine pasta and shrimp: Add the drained pasta to the skillet, tossing in the garlic butter sauce. Add a splash of reserved pasta water if the sauce needs loosening. Return the shrimp to the pan and toss until everything is well coated.
Finish with parsley: Stir in freshly chopped parsley. Taste and adjust seasoning with extra salt, pepper, or lemon juice.
Serve immediately: Plate the pasta and top with extra parsley and Parmesan cheese if desired. Serve with lemon wedges on the side.