Cook the Pasta:
Bring a large pot of salted water to a boil. Cook linguine until al dente. Reserve ½ cup pasta water, then drain and set aside.

Sauté the Shrimp:
While pasta cooks, heat olive oil and butter in a large skillet over medium heat. Add shrimp in a single layer, season with salt and pepper, and cook for 1–2 minutes per side until pink. Remove from skillet and set aside.

Make the Lemon Cream Sauce:
In the same skillet, sauté garlic for 30 seconds until fragrant. Add heavy cream and bring to a gentle simmer. Stir in Parmesan cheese until melted. Add lemon zest, lemon juice, salt, pepper, and red pepper flakes (if using).

Combine Pasta and Shrimp:
Add cooked linguine and shrimp back to the skillet. Toss until coated. If the sauce is too thick, add a splash of reserved pasta water to loosen.

Serve:
Plate immediately and garnish with fresh parsley and extra Parmesan, if desired.