Bring a large pot of salted water to a rolling boil and cook the pasta until al dente. I always save about half a cup of pasta water before draining. This starchy water helps bring the sauce together later. Set the pasta aside while you work on the shrimp.
Pat the shrimp dry and season them lightly with salt and black pepper. Heat olive oil and half of the butter in a large skillet over medium heat. Cook the shrimp for about 1–2 minutes per side until pink and opaque, then remove them from the pan to avoid overcooking.
In the same skillet, add the remaining butter and minced garlic. Let the garlic cook gently until fragrant, not browned. Stir in red chili flakes if using, then pour in the heavy cream and let it simmer for a couple of minutes until slightly thickened.
Add the cooked pasta directly into the skillet with the sauce. Toss gently, adding a splash of reserved pasta water if needed to loosen the sauce. Return the shrimp to the pan and let everything warm together for a minute.
Turn off the heat and stir in freshly grated Parmesan cheese and lemon juice. Taste and adjust seasoning if needed. Sprinkle chopped parsley on top and serve immediately while it’s warm and glossy.