Cook pasta in salted water until al dente and reserve 1/2 cup pasta water, then drain.
Season shrimp with salt and pepper.
Heat olive oil and 1 tbsp butter in a skillet and cook shrimp 1–2 minutes per side, then remove.
Add remaining butter and garlic and sauté 30 seconds until fragrant (don’t burn it).
Pour in heavy cream, stir, and simmer 2–3 minutes until slightly thick.
Stir in parmesan until smooth, then loosen with pasta water if needed.
Add cooked pasta and shrimp back to the skillet and toss until coated.
Finish with lemon juice, parsley, and extra parmesan, then serve hot.