Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Just before draining, reserve about 1 cup of the starchy pasta water, then drain the pasta.
While the pasta is cooking, pat the shrimp dry with paper towels and season lightly with salt and pepper.
In a large skillet over medium heat, melt the butter with the olive oil. Add the minced garlic and red pepper flakes (if using) and cook for about 30-60 seconds until fragrant, being careful not to burn the garlic.
Increase the heat to medium-high, add the shrimp to the skillet in a single layer. Cook for 1-2 minutes per side, until they are pink and opaque. Do not overcook. Remove the shrimp from the skillet and set aside on a plate.
Reduce the heat to medium. Pour the white wine (or chicken broth) into the skillet to deglaze, scraping up any browned bits from the bottom of the pan. Let it simmer and reduce by about half, which should take about 2 minutes.
Stir in the heavy cream, lemon juice, and lemon zest. Bring to a gentle simmer and cook for 2-3 minutes, until the sauce has slightly thickened. Season with salt and pepper to taste.
Add the drained pasta directly to the skillet with the sauce. Toss well to coat. If the sauce is too thick, add a splash of the reserved pasta water until it reaches your desired consistency.
Return the cooked shrimp to the pan, along with the Parmesan cheese and fresh parsley. Toss everything together until the shrimp is heated through and the cheese is melted into the sauce.
Serve immediately, garnished with extra Parmesan cheese and fresh parsley if desired.
Notes
Chef's Tips: For the best sauce, don't skip reserving the pasta water. The starch in the water helps the sauce cling to the pasta beautifully. Variations: Feel free to add 2 cups of fresh spinach to the sauce at the same time as the heavy cream and allow it to wilt for extra nutrients. Storage: Store leftovers in an airtight container in the refrigerator for up to 2 days. Reheat gently on the stovetop with a splash of milk or cream to loosen the sauce.