1. Preheat your grill to medium-high heat.
2. In a mixing bowl, combine the chopped salmon, breadcrumbs, beaten egg, 2 tablespoon mayonnaise, Dijon mustard, lemon juice, chopped basil, salt, and pepper. Mix well.
3. Form the mixture into 4 patties.
4. Grill the patties for about 4-5 minutes on each side, or until fully cooked.
5. While the patties are grilling, prepare the lemon basil mayo. In a small bowl, mix together ½ cup mayonnaise, lemon juice, chopped basil, garlic powder, and salt.
6. Serve the salmon burgers on buns with a generous dollop of lemon basil mayo.