Pat the shrimp dry with paper towels and season lightly with salt and freshly ground black pepper.
Heat 2 tablespoons of butter and 2 tablespoons of olive oil in a large skillet over medium-high heat until the butter is melted and the mixture is hot.
Add the shrimp to the skillet in a single layer and cook for 2 minutes without moving them, until the underside is pink and slightly golden.
Flip the shrimp and cook for an additional 1 to 2 minutes until fully opaque and cooked through. Remove the shrimp from the skillet and set aside on a plate.
Reduce the heat to medium and add the minced garlic and red pepper flakes to the skillet. Sauté for about 1 minute until fragrant, stirring constantly to prevent burning.
Pour in the chicken broth, lemon juice, and lemon zest. Stir and let the sauce simmer for 2 to 3 minutes until slightly reduced.
Add the remaining 1 tablespoon of butter to the skillet and stir 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 another 1 minute to warm the shrimp through.
Remove from heat and sprinkle the chopped fresh parsley over the shrimp scampi.
Serve immediately over cooked pasta, rice, or with crusty bread to soak up the sauce.