Cook pasta according to the package instructions, reserving some of the pasta water, if desired. Keep warm.
While the pasta is cooking, season the shrimp with a pinch of salt and pepper. In a large skillet over medium heat, melt 1 tablespoon of the butter. Add the shrimp and cook for 2 minutes. Flip and cook for another 2-3 minutes, or until they are pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet over low heat, melt the remaining 4 tablespoons of butter. Stir in the heavy cream, and the salt, pepper, and nutmeg. Bring to a simmer.
Remove the saucepan from the heat and stir in the parmesan cheese. Return the saucepan to low heat and bring it back just to a simmer, stir until the cheese is melted and the sauce is smooth. Adjust seasoning with salt and pepper, if necessary.
Add the cooked pasta and shrimp to the sauce and toss to coat thoroughly, adjusting the consistency of the sauce with reserved pasta water or additional cream, if needed. Garnish with additional parmesan cheese and chopped parsley, if desired.
