Cook fettuccine according to the instructions on box, reserving a cup of pasta water to thicken the sauce, if needed. In a large skillet over medium heat, heat 1 tablespoon butter until melted. Add shrimp, season with salt and pepper and cook until pink and completely opaque, 2 to 3 minutes per side. Remove shrimp from skillet and set aside. Into the pan, add remaining 2 tablespoons butter and garlic. Cook until the garlic becomes fragrant, about 1 minute. Whisk in flour and cook until no longer raw, 2 minutes. Stir in heavy cream and milk, then whisk in egg yolk.  Bring to a low simmer and whisk in parmesan. When cheese is melted and sauce has thickened slightly, add cooked pasta and shrimp, tossing to combine. Season with salt and pepper. Garnish with more parmesan and parsley.