Any recommendations on cooking large Shrimp on the BBQ? Looking to mix it up not the old cajun seasoning bit!?

Try grilled scampi. It’s great!

Grilled Shrimp Scampi
Shrimp marinated in lemon, garlic, and parsley for 30 minutes, then grilled. Can be used as an appetizer or main dish.
1/4 cup olive oil
1/4 cup lemon juice
3 Tbs chopped fresh parsley
1 Tbs minced garlic
ground black pepper to taste
crushed red pepper flakes to taste (optional)
1 1/2 lbs medium shrimp, peeled and deveined
1 In a large, non-reactive bowl, stir together the olive oil, lemon juice, parsley, garlic, and black pepper. Season with crushed red pepper, if desired. Add shrimp, and toss to coat. Marinate in the refrigerator for 30 minutes.
2 Preheat grill for high heat. Thread shrimp onto skewers, piercing once near the tail and once near the head. any remaining marinade.
3 Lightly oil grill grate. Grill for 2 to 3 minutes per side, or until opaque.
Servings: 6

Caribbean Grilled Shrimp With Mango Salsa
1 to 1 1/2 lbs large shrimp, peeled and deveined
Marinade
1 tsp ground allspice
1/2" piece ground cinnamon stick
1 tsp black pepper, ground
1/4 tsp freshly grated nutmeg
1/2 small red onion
4 green onions
1 clove garlic
1/2 jalapeno pepper, seeds removed
1/2 tsp salt (or less)
2 Tbs soy sauce
1/4 cup vegetable oil
Mango Salsa
2 ripe mangos, peeled and cut into 1/4" cubes
1/2 jalapeno pepper, seeded and finely chopped
1/2 small red onion, finely chopped
4 Tbs chopped cilantro
Zest of one lime
Juice of two limes
1 tsp sugar
Whip up all the Marinade ingredients in a food processor Coat the shrimp well with the marinade for at least half a day. Soak the skewers in water for half an hour. Skewer the shrimp and cook over a hot grill or hot coals for about a minute and a half on each side, then serve with the mango salsa. Use up all the salsa as it doesn’t keep well.
Servings: 6

Grilled Texas Shrimp
1/4 cup vegetable oil
1/4 cup tequila
1/4 cup red wine vinegar
2 Tbs Mexican lime juice
1 Tbs ground red chiles
1/2 tsp salt
2 cloves garlic, finely chopped
1 red bell pepper, finely chopped
24 large raw shrimp, peeled and de-veined (tails left on)
6 (8-inch size) metal skewers
1 Mix all ingredients except shrimp in shallow glass or plastic dish. Stir in shrimp. Cover and refrigerate for 1 hour.
2 Remove shrimp from marinade, reserving marinade. Thread 4 shrimp on each skewer. Grill over medium coals, turning once, until pink, 2 to 3 minutes on each side.
3 Heat marinade to boiling in a non-reactive saucepan. Reduce heat to low. Simmer uncovered until bell pepper is tender, about 5 minutes. Serve with shrimp.
4 To broil: place the skewered shrimp on a broiler pan rack. Broil with tops about 4 inches from heat, turning once, until pink, 2 to 3 minutes on each side.
Servings: 6

Marinated Grilled Shrimp
3 cloves garlic, minced
1/3 cup olive oil
1/4 cup tomato sauce
2 Tbs red wine vinegar
2 Tbs chopped fresh basil
1/2 tsp salt
1/4 tsp cayenne pepper
2 lbs fresh shrimp, peeled and deveined
1 In a large bowl, stir together the garlic, olive oil, tomato sauce, and red wine vinegar. Season with basil, salt, and cayenne pepper. Add shrimp to the bowl, and stir until evenly coated. Cover, and refrigerate for 30 minutes to 1 hour, stirring once or twice.
2 Preheat grill for medium heat. Thread shrimp onto skewers, piercing once near the tail and once near the head. Discard marinade.
3 Lightly oil grill grate. Cook shrimp on preheated grill for 2 to 3 minutes per side, or until opaque.
Servings: 6