Pat the shrimp dry with paper towels and season with kosher salt and black pepper.
Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat until the butter is melted and the mixture is hot but not smoking.
Add the shrimp to the skillet in a single layer and cook for 2 minutes without stirring, until the shrimp start to turn pink on one side.
Flip the shrimp and cook for another 1 to 2 minutes until fully pink and opaque. Remove the shrimp from the skillet and set aside on a plate.
Reduce the heat to medium and add the minced garlic and crushed red pepper flakes to the skillet. Sauté for about 30 seconds until fragrant, stirring constantly to prevent burning.
Pour in the dry white cooking broth and fresh lemon juice, scraping the bottom of the skillet with a wooden spoon to loosen any browned bits. Let the sauce simmer for 2 minutes to reduce slightly.
Stir in the remaining 1 tablespoon of butter until melted and the sauce is smooth.
Return the cooked shrimp to the skillet and toss to coat them evenly in the sauce. Cook for an additional 1 minute to warm through.
Remove the skillet from heat and sprinkle the chopped fresh parsley and lemon zest over the shrimp. Toss gently to combine.
Serve immediately over cooked pasta or with crusty bread to soak up the sauce.