Cook the pasta according to package instructions in a large pot of salted water until al dente. Reserve 1/2 cup of pasta water before draining.
Pat the shrimp completely dry with paper towels and season with salt and pepper. This ensures they’ll sear properly rather than steam.
Heat 2 tablespoons of butter and olive oil in a large skillet over medium-high heat until butter is melted and slightly bubbling.
Add shrimp to the hot pan in a single layer and cook for 1-2 minutes per side until pink and opaque. Remove shrimp to a plate and set aside.
Reduce heat to medium and add remaining butter to the same pan. Once melted, add minced garlic and red pepper flakes (if using) and cook for 30 seconds until fragrant, being careful not to burn the garlic.
Pour in the white wine and scrape up any browned bits from the bottom of the pan with a wooden spoon. Let the liquid reduce by half, about 2 minutes.
Slowly stir in the heavy cream and bring to a gentle simmer. Cook for 3-4 minutes until the sauce begins to thicken slightly.
Reduce heat to low and gradually whisk in the Parmesan cheese until melted and incorporated into a smooth sauce.
Add lemon juice, zest, and half the parsley to the sauce, stirring to combine. Taste and adjust seasoning with salt and pepper.
Return the cooked shrimp to the pan and gently toss to coat in the sauce. If the sauce seems too thick, add a splash of the reserved pasta water.
Add the drained pasta directly to the sauce and toss everything together using tongs until the pasta is evenly coated and everything is well combined.
Serve immediately, garnished with remaining parsley, extra Parmesan cheese, and black pepper.