Pat the shrimp dry. Moisture is the enemy of a good sear. Lay shrimp on paper towels and pat both sides until dry.
Season generously. Toss shrimp with 1 tablespoon olive oil, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and lemon pepper if using. Set aside while the pan heats.
Preheat the skillet. Place a large skillet over medium-high heat and add the remaining 1 tablespoon olive oil and 1 tablespoon butter.
When the butter foams, the pan is ready.
Sear the shrimp in batches. Add half the shrimp in a single layer. Cook 1–2 minutes per side until just opaque with pink edges. Transfer to a plate.
Repeat with the remaining shrimp. Do not overcook.
Lower the heat and build the sauce. Reduce heat to medium. Add 2 tablespoons butter and the garlic.
Sauté 30 seconds until fragrant, stirring often so the garlic doesn’t brown.
Deglaze and brighten. Stir in broth, lemon juice, and lemon zest. Scrape up any browned bits from the pan. Simmer 1–2 minutes to reduce slightly and meld the flavors.
Add gentle heat. Sprinkle in red pepper flakes if using.
Taste and adjust salt and pepper. The sauce should taste bright and buttery with a hint of garlic.
Finish the dish. Return shrimp and any juices to the skillet. Toss to coat and warm through, about 30–60 seconds.
Turn off the heat and swirl in the final 1 tablespoon butter for a silky finish.
Garnish and serve. Sprinkle with parsley and serve with lemon wedges. Pair with your favorite low-carb side to catch the extra sauce.