In a large, deep skillet or Dutch oven, heat the olive oil and 1 tablespoon of butter. Add the shrimp in a single layer and sear for 1–2 minutes per side until pink and opaque. Remove the shrimp and set aside; this prevents them from becoming rubbery during the pasta boil.
In the same pan, add the remaining butter and the minced garlic. Sauté for 30 seconds until fragrant, being careful not to brown the garlic.
Pour in 2 cups of water (or chicken broth) and the heavy cream. Bring the mixture to a gentle boil.
Add the dry fettuccine noodles directly into the pan. Submerge them as much as possible. Simmer over medium heat, stirring frequently with tongs to prevent the noodles from sticking together. The pasta will cook in the cream and water, releasing starch that naturally thickens the sauce.
Once the pasta is al dente and the liquid has reduced into a thick sauce, turn the heat to low. Stir in the freshly grated Parmesan cheese, lemon zest, and red pepper flakes.
Add the cooked shrimp back into the pan. Toss everything gently until the shrimp are reheated and the sauce is glossy and clings to every strand of pasta.
Garnish with fresh parsley and a final dusting of Parmesan.