01 - Preheat oven to 425°F. Line a baking sheet with parchment paper or lightly grease with cooking spray.
02 - Slice each shrimp along the back curve, cutting deep but not all the way through. Arrange them cut side up on the prepared baking sheet.
03 - In a medium bowl, gently fold together the lump crab meat, mayonnaise, beaten egg, Dijon mustard, Worcestershire sauce, Old Bay seasoning, black pepper, diced celery, diced red bell pepper, chopped parsley, and panko breadcrumbs. Mix until just combined — do not overwork the filling or it will become dense.
04 - Scoop 1 to 2 tablespoons of the crab mixture, shape into a small oval, and press it firmly into the opened back of each butterflied shrimp. Secure with toothpicks if needed to hold the filling in place. Repeat until all shrimp are filled.
05 - Melt the butter in a small saucepan over low heat. Stir in the lemon juice, minced garlic, parsley, chives, smoked paprika, cayenne pepper, red pepper flakes, kosher salt, and a generous pinch of black pepper. Keep warm on the lowest heat setting.
06 - Using a pastry brush, lightly coat each stuffed shrimp with some of the cowboy butter. Bake on the center rack for 14 to 16 minutes, until the shrimp turn opaque pink and the crab filling turns golden.
07 - Switch the oven to broil for the final 1 to 2 minutes to develop a deeper golden crust on the crab filling. Watch closely to prevent burning.
08 - Remove the shrimp from the oven and immediately drizzle generously with the reserved warm cowboy butter. Remove any toothpicks before serving. Plate with lemon wedges and pass extra cowboy butter on the side.