Bring a large pot of well-salted water to a boil. Cook the pasta until just shy of al dente. Reserve 1/2 cup of pasta water, then drain.
Pat the shrimp dry and season lightly with salt and pepper.
Heat the olive oil and 1 tablespoon butter over medium-high heat. Sear the shrimp for about 45 seconds per side, just until pink. Transfer to a plate.
Reduce the heat to medium. Add the remaining butter, garlic, and red pepper flakes. Cook for about 30 seconds until fragrant.
Pour in the white wine and simmer for 5-6 minutes until reduced by about half.
Stir in the lemon zest, then the lemon juice, followed by the heavy cream. Bring to a gentle simmer.
Add a few splashes of reserved pasta water at a time, then stir in the Parmesan until smooth and creamy.
Fold in the parsley, then add the cooked pasta and toss until it’s all coated in the sauce.
Return the shrimp to the pan and toss just until warmed through.
Finish with extra Parmesan, parsley, and a little more lemon zest if desired.