Boil the pasta: Bring a large pot of salted water to a boil.
Cook the pasta until just shy of al dente. Reserve 3/4 cup of the starchy pasta water, then drain.
Season the shrimp: Pat the shrimp dry. Season with salt, pepper, and a pinch of red pepper flakes if using.
Sauté the shrimp: In a large skillet, heat 1 tablespoon olive oil and 1 tablespoon butter over medium-high heat.
Add half the shrimp in a single layer and cook 1–2 minutes per side until just pink. Transfer to a plate. Repeat with remaining shrimp, adding another splash of oil if needed.
Sauté the aromatics: Reduce heat to medium.
Add the remaining butter and olive oil. Stir in the garlic and cook 30–60 seconds until fragrant, not brown.
Deglaze: Pour in the white wine (or broth) and scrape up any browned bits. Let it simmer for 1–2 minutes to reduce slightly.
Add lemon: Stir in the lemon zest and juice.
Taste and season with salt and pepper.
Build the sauce: Add the drained pasta and 1/2 cup of the reserved pasta water. Toss vigorously until the sauce turns glossy and clings to the noodles. If it looks dry, add more pasta water a splash at a time.
Finish with shrimp and cheese: Return the shrimp and any juices to the pan.
Toss in the Parmesan and parsley. Warm through for 1–2 minutes. Adjust salt, pepper, and lemon to taste.
Serve: Plate with extra Parmesan, a pinch of red pepper flakes, and lemon wedges on the side.