Start heating the pasta water. Fill a large saucepan with water and season with about 1 tablespoon kosher salt. Bring to a boil over medium-high heat (this will take about 15 minutes — enough time to prepare the rest of the recipe).
Get ready to cook. Shrimp scampi is very quick cooking, so be sure to have everything ready before you begin cooking the pasta or making the sauce. The shrimp should be thawed if frozen and peeled with the tails removed. Grate 2 cloves of garlic and thinly slice the other 2. Remove a 1-inch section of peel from the lemon and then juice it. Measure the olive oil. Finally, chop the parsley.
Marinate the shrimp. Place the shrimp, grated garlic, olive oil, and 1 teaspoon kosher salt in a large bowl and toss to combine; set aside.
Add the pasta to the pasta water. Add the linguine to the boiling water and reduce the heat slightly to maintain a simmer. Set a timer for 8 minutes.
Fry the garlic, lemon zest, red pepper flakes. Melt 2 tablespoons of the butter in a large, straight-sided skillet over medium-low heat. When the butter begins to bubble, add the sliced garlic, the strip of lemon peel, and red pepper flakes and sauté until fragrant, about 2 minutes.
Add the lemon juice and reduce the sauce. Carefully add the lemon juice. There will be plenty of steam at first, and then the whole pan will come to a steady simmer. Scoop 1/4 cup of pasta cooking water from the saucepan into the sauce and cook until the butter sauce reduces slightly, about 2 minutes.
Add the remaining butter to the sauce and whisk to emulsify. Quickly add the remaining 2 tablespoons of butter to the reduced sauce. Whisk briskly until the sauce is lightened in color and thickened, about 1 minute.
Add the shrimp to pan and cook. Add the shrimp to the sauce and cook, stirring regularly, until the shrimp is opaque, about 3 minutes. Remove the pan from the heat until the pasta is ready.
Drain the pasta and add to the pan, toss with tongs. Check the pasta when the timer goes off. When it is tender, drain. Add the pasta to the shrimp, tossing with tongs to coat the pasta with the sauce.
Add the parsley and serve immediately. Remove the lemon peel from the pan. Add the parsley and toss again to coat. Serve immediately.