Step 1
Peel shrimp and place into a mixing bowl; set shrimp shells aside in a saucepan.
Step 2
Drizzle vegetable oil over shrimp and season with black pepper smoked paprika cayenne pepper and seafood seasoning. Mix shrimp to coat with spices and cover bowl with plastic wrap; refrigerate shrimp to absorb flavors at least 1 hour.
Step 3
Place reserved shrimp shells in saucepan over medium-high heat with 1 tablespoon butter; cook and stir until shells are pink and fragrant 1 to 2 minutes. Pour in chicken stock bring to a boil and reduce heat to low; simmer until shrimp shells have given off their flavor 20 to 30 minutes.
Step 4
Strain shrimp stock through a fine mesh strainer into a bowl and add lemon juice Worcestershire sauce and hot sauce. Stir to combine.
Step 5
Place a large skillet over high heat until pan is very hot; sear shrimp in the very hot dry pan until shrimp are browned about 1 minute per side.
Step 6
Stir 3 tablespoons cold butter garlic and minced rosemary into shrimp; cook and stir until shrimp are opaque in the middle and garlic is fragrant 1 minute. Pour in shrimp stock.
Step 7
Transfer shrimp from skillet to a bowl using a slotted spoon; reserve sauce in skillet. Bring sauce to a boil and cook until reduced slightly about 5 minutes. Adjust seasoning to taste. Return shrimp to pan reduce heat to low and warm through about 1 minute. Serve shrimp drizzled with pan sauce; garnish with a rosemary sprig.