Prep the Shrimp: Take your thawed shrimp and place it on a plate lined with paper towels. Pat the tops completely dry, then season both sides lightly with kosher salt and black pepper.
Sizzle the Aromatics: Place a large skillet over medium heat. Add the olive oil and 2 tablespoons of unsalted butter. Once melted, add the finely minced garlic and red pepper flakes. Cook for exactly 1 minute, stirring constantly so the garlic does not burn.
Sear the Shrimp: Turn the heat up to medium-high and add the shrimp to the skillet in a single layer. Cook undisturbed for 2 minutes, then flip each piece and cook the other side for 1 to 2 minutes until pink and opaque. Transfer the shrimp onto a clean plate immediately.
Reduce the Liquid: Pour the chicken stock (or wine) and fresh lemon juice into the hot skillet. Use a wooden spoon to scrape up any browned bits from the bottom. Let it simmer for about 3 minutes until reduced by half.
Make the Glossy Sauce: Turn the stove down to its lowest heat setting. Add the remaining 2 tablespoons of cold, cubed butter and the fresh lemon zest into the liquid. Whisk continuously until a thick, glossy sauce forms.
Toss and Serve: Add the cooked pasta, the seared shrimp, and the finely chopped fresh parsley back into the skillet. Gently toss everything together for 60 seconds until coated in the sauce. Serve immediately with fresh lemon wedges.