Cook fettuccine until al dente (follow package instructions for best results). Set pasta aside and save about 1/2 a cup of the pasta water in case you need it to thin your sauce.
Preheat the skillet with 2 tbsp of butter. Season shrimp with salt and cook until they turn pink and form a crust on the outside. Remove from the pan and set aside.
To the same pan, add the rest of the butter, heavy cream, garlic, and parmesan cheese. Bring it to a light simmer over low-heat.
Add in fettuccine and toss.
Add in shrimp and lightly toss. Remove from heat. If the sauce thickens more than you like, add a little bit of that pasta water to thin it out. If it's too thin, let it sit at room temperature for a couple of minutes until it thickens.