Pre-heat a large heavy bottom pan on medium-high heat and add olive oil. Toss in the shrimp and arrange in a single layer; season with 1 teaspoon salt and freshly ground black pepper.
Continue cooking and simmering on low heat for 5 minutes to reduce the sauce. Season with lemon zest, 1 teaspoon salt, and pepper to taste. Add the freshly grated parmesan cheese and stir to combine. Remove from the stove top and set aside.
Bring a large pot of salted water to boil and add the fettuccine. Cook according to package instructions until al dente (each brand of fettuccine might have slightly different cooking times).