Prepare the Aioli: In a small bowl, combine capers, mayonnaise, lemon juice, dill, and garlic. Mix well and season with salt and black pepper to taste. Set aside.
Preheat and Prepare the Grill: Preheat a grill or grill pan over medium heat. Lightly grease one side of the salmon fillets with nonstick spray and season with salt and black pepper.
Cook the Salmon: Place the greased side of the salmon down on the grill. While it cooks, season the other side and grease lightly with nonstick spray. Cook for about 5 minutes or until grill marks appear. Flip and continue cooking until the salmon reaches an internal temperature of 125°F (51°C) for a medium-rare finish. Once cooked, set the salmon aside to rest for 3–5 minutes.
Toast the Buns: While the salmon is cooking, toast the brioche buns on the grill, toaster oven, or broiler until lightly golden.
Assemble the Sandwich: Spread the prepared aioli on the inside of both halves of each toasted bun. Layer each sandwich with butter lettuce, tomato slices, cooked salmon, and red onion.
Serve: Plate the sandwiches with pita chips, hummus, pickle spears, and a glass of apple juice. Enjoy!