All ingredients ready? Let's begin!
Bring a large pot of water to a boil over high heat. Add the kosher salt and stir to dissolve. Add the linguini and cook to al dente, about 1 minute shy of the package directions. Reserve 1 cup of the cooking liquid. Drain the pasta in a colander.
While the pasta is cooking, sauté the shrimp. In a large skillet over medium-high heat, warm the olive oil. Add the shrimp and cook for about 1 minute until they start to turn pink on the bottom. Stir in the garlic and cook for approximately 2 minutes longer until the garlic is fragrant and the shrimp is pink but not overcooked. Transfer the shrimp to a serving bowl and set aside.
Return the pan to the burner and reduce the heat to medium. Add the cream, lemon zest, and cayenne to the skillet and bring to a rolling simmer. Turn the heat down to low and allow the cream to simmer until slightly reduced, approximately 2 minutes.
Add the butter to the cream and whisk until it melts completely and is incorporated into the cream. Stir in the lemon juice and remove the pan from the heat.
Add the parmesan and stir until it melts into the sauce. Season to taste with salt and pepper.
Add the linguini to the sauce and toss to coat evenly. Thin the sauce with a little of the pasta water if needed.
Toss the shrimp with the pasta and transfer the pan contents to the serving bowl. Garnish with parsley and serve while warm.