Bring a large pot of well-salted water to a boil. Cook the pasta al dente according to package directions (typically 8–11 minutes). Reserve 1 cup of pasta water, then drain.

Pat shrimp dry and season lightly with salt and pepper.

In a large skillet over medium-high heat, add 1 tablespoon of olive oil and 1 tablespoon of butter. When hot, add shrimp in a single layer and cook for 2–3 minutes per side until pink and opaque. Transfer shrimp to a plate.

Reduce heat to medium, add remaining butter and olive oil. Add minced garlic and sauté for 30–45 seconds until fragrant (do not brown).

Pour in chicken broth and heavy cream. Add cream cheese pieces if using. Stir and simmer gently for 4–6 minutes until the sauce slightly thickens.

Stir in grated Parmesan a little at a time until melted and the sauce is silky. If sauce is too thick, add reserved pasta water 1–2 tablespoons at a time until you reach desired consistency.

Stir in lemon zest and juice, red pepper flakes (if using), and taste for seasoning—add salt and pepper as needed.

Add shrimp back to the skillet and toss to coat for 1–2 minutes to reheat. Then, add drained pasta and toss well to combine, adding a splash more pasta water if needed to loosen.

Serve immediately with chopped parsley, extra Parmesan, and a lemon wedge.