Cook Pasta: Boil linguine in salted water until al dente. Reserve ¼ cup of pasta water before draining.
Sauté Shrimp: Pat shrimp dry and season with salt and black pepper. Heat 1 tbsp butter and 1 tbsp olive oil in a pan over medium-high heat. Cook shrimp for 2 minutes per side until pink and opaque. Remove from pan.
Prepare Sauce: In the same pan, add garlic and red pepper flakes, cooking for 30 seconds until fragrant. Deglaze with white wine, scraping up browned bits. Let simmer for 2 minutes.
Combine Everything: Add pasta water, lemon juice, and lemon zest. Toss in drained pasta, stirring well. Add shrimp back to the pan along with remaining butter and parsley. Mix until coated.
Serve: Plate the pasta, sprinkle with Parmesan, and garnish with extra parsley and red pepper flakes if desired.