Bring a large pot of salted water to a rolling boil. Add the fettuccine and cook until just al dente, about 8 minutes. Drain, reserving a little pasta water, and set aside.
Meanwhile, pat the shrimp dry and season lightly with salt and pepper. Heat a tablespoon of olive oil in a large skillet over medium-high heat. Add the shrimp in a single layer and sear for about 2 minutes without moving, until they turn pink and develop a slight char.
Flip the shrimp and cook for an additional 1-2 minutes until fully opaque and tender. Remove from the skillet and set aside.
In the same skillet, lower the heat to medium. Add the butter and minced garlic; sauté until fragrant, about 30 seconds. The garlic should smell sweet and toasty without burning.
Pour in the heavy cream and bring to a gentle simmer, stirring constantly. Let it cook for 2-3 minutes until slightly thickened and glossy, scraping up any browned bits from the bottom.
Stir in the grated Parmesan cheese until melted and smooth, then squeeze in a bit of lemon juice and zest for brightness. Adjust seasoning with salt and pepper as needed.
Add the cooked shrimp back into the skillet, tossing gently to coat them evenly with the sauce. If the sauce is too thick, stir in a splash of reserved pasta water to loosen it up.
Finally, add the drained fettuccine to the skillet and toss until the pasta is well coated with the sauce. The sauce should be silky, glossy, and cling to each strand of pasta.
Serve immediately, garnished with extra Parmesan and a squeeze of lemon if desired. The dish should be hot, creamy, with tender shrimp and a bright, briny aroma.
