Bring a large pot of salted water to a rolling boil and cook the fettuccine until just al dente, about 8 minutes. Drain and toss with a little oil to prevent sticking, then set aside.
While the pasta cooks, season the shrimp with salt, pepper, and a pinch of paprika if desired. Heat olive oil in a heavy-bottomed skillet over medium-high heat. Once shimmering, add the shrimp and sauté for 2-3 minutes on each side until they turn bright pink and opaque. Remove the shrimp and set aside.
In the same skillet, lower the heat to medium. Add the butter and minced garlic, cooking for about 30 seconds until fragrant and just starting to turn golden. Pour in the heavy cream, stirring gently to incorporate any browned bits from the pan. Bring the cream to a gentle simmer, watching for small bubbles around the edges.
Gradually sprinkle in the grated Parmesan cheese, whisking constantly until the sauce becomes smooth and thickened, about 2-3 minutes. If the sauce gets too thick, add a splash of reserved pasta water or milk to loosen it up.
Return the cooked shrimp to the skillet, tossing gently to coat them in the creamy sauce. Add a squeeze of fresh lemon juice to brighten the flavors. Taste and adjust seasoning with salt and pepper as needed.
Gently add the drained fettuccine to the skillet, tossing with tongs until all the pasta is evenly coated with the sauce and the shrimp are well distributed. Let everything heat together for another minute.
Remove from heat and serve immediately, garnished with extra Parmesan and freshly ground black pepper for a final touch. The sauce should be silky, the shrimp tender, and the pasta coated in a glossy, cheesy layer.
