Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente. Reserve 0.5 cup of pasta water before draining.
Pat shrimp dry and season with half of the salt and pepper.
In a large skillet, heat olive oil and 1 tablespoon of butter over medium-high heat.
Add shrimp to the skillet in a single layer and cook for 2 minutes per side until opaque. Remove shrimp from skillet and set aside.
Reduce heat to medium and add the remaining 1 tablespoon of butter and minced garlic to the skillet. Sauté for 60 seconds until fragrant.
Pour in the heavy cream and red pepper flakes. Bring to a simmer and cook for 3 minutes until slightly reduced.
Whisk in the Parmesan cheese until the sauce is smooth and cheese is fully melted.
Add the cooked pasta and shrimp back into the skillet. Toss to coat thoroughly, adding reserved pasta water 1 tablespoon at a time if needed to adjust consistency.
Garnish with fresh parsley and serve immediately.