In a medium-sized saucepan, boil water and salt it. Add the pasta and cook according to the package instructions until al dente. Reserve 1 cup of the pasta water, then drain the pasta.
In a skillet over medium heat, melt 1 tablespoon of the butter and add the olive oil. Cook the shrimp for a minute, then season with salt, pepper, and Old Bay seasoning if using.
Continue to cook the shrimp until pink. Do this in batches if needed to avoid overcrowding. Remove the shrimp to a plate and set aside.
In the same pan, melt the remaining butter and add the garlic. Cook for 30 seconds until fragrant. Add the heavy cream and deglaze the pan with a spatula.
Add the Parmesan and let it melt, then loosen the sauce with reserved pasta water and allow to simmer for a minute. Taste and adjust salt and pepper as needed.
Toss the pasta with the sauce until well coated. Add the shrimp back in to reheat gently. Garnish with freshly chopped parsley and serve.