Chef John's New Orleans-Style Barbequed Shrimp

Ingredients (15)

• + 1 ½ pounds colossal shrimp, EZ-peel type (deveined and shells split down the back) add to pantry
• + 1 ½ tablespoons vegetable oil add to pantry
• + 1 tablespoon freshly ground black pepper, or to taste add to pantry
• ✓ ¼ teaspoon smoked paprika
• + ⅛ teaspoon cayenne pepper add to pantry
• ✓ ⅛ teaspoon seafood seasoning (such as Old Bay®)
• + 1 tablespoon butter add to pantry
• + 2 cups chicken stock add to pantry
• + lemon, juiced add to pantry
• + 2 tablespoons Worcestershire sauce, or more to taste add to pantry
• + 2 dashes hot sauce, or to taste add to pantry
• + 3 tablespoons cold butter, cut into chunks add to pantry
• ✓ 6 cloves garlic, minced
• + 1 tablespoon minced fresh rosemary add to pantry
• + 1 sprig fresh rosemary for garnish add to pantry