Bring a large pot of water to a boil and salt it well. Add the pasta and cook until al dente, according to package instructions. Drain in a colander.
Meanwhile, heat olive oil in a large skillet over medium-high heat. Add the shrimp season with 1/2 tsp kosher salt and a few cracks of pepper.
Cook until they turn pink and opaque, about 2-3 minutes per side. Remove the shrimp from the skillet and set aside. Don't wipe out the pan.
In the same skillet, reduce the heat to medium and melt the butter. Add the minced garlic and cook until fragrant, a 1 minute, scraping up any browned bits from the pan as you stir.
Whisk in the heavy cream, lemon zest, 1/2 tsp more kosher salt and a few cracks of black pepper. Bring to a simmer and then remove the skillet from the heat.
Off of the heat, whisk in the parmesan cheese until the sauce is smooth. Stir in lemon juice.
Add the cooked pasta and shrimp to the skillet with the sauce. Toss to coat everything evenly. Serve immediately, garnished with minced chives or parsley.
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Notes
For a slightly lighter version, you can use half-and-half instead of heavy cream.If you prefer, you can use pre-cooked shrimp. Just add them to the sauce to heat through before tossing with the pasta.Substitute parmesan with pecorino romano for a different flavor.Store leftovers in an airtight container in the refrigerator for up to 2 days. Reheat gently on the stovetop, adding a splash of cream or milk to loosen the sauce if needed.For a pretty presentation, set aside some of the browned shrimp to top individual portions at the end.