Bring a large pot of generously salted water to a boil. Cook the linguine or fettuccine until just al dente according to the package directions, reserve 1/2 cup of the cooking water, and drain.

Pat the shrimp dry and season lightly with salt and pepper. Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat, then cook the shrimp for approximately 1–2 minutes per side until pink and opaque; transfer them to a plate.

Reduce the skillet heat to medium and add the remaining tablespoon of butter and the minced garlic. Cook for about 30–60 seconds, stirring often, until fragrant but not browned.

Pour in the heavy cream and add the lemon zest, black pepper, and optional red-pepper flakes. Simmer gently for 2–3 minutes so the cream warms and the garlic and citrus aromas infuse the sauce.

Lower the heat and whisk in the finely grated Parmesan. Add a little reserved pasta water, a splash at a time, until the sauce becomes smooth and loose enough to coat the pasta.

Add the drained pasta to the skillet and toss until every strand is coated. Stir in the lemon juice over low heat or after removing the pan from the burner to keep the cream sauce smooth.

Return the shrimp to the skillet and warm everything briefly for about 1 minute. Finish with chopped parsley and adjust with additional Parmesan, black pepper, or lemon juice as desired.