Place the salmon, shallots, mustard, capers, dill, lemon juice, salt, and pepper, in a food processor.
Blend until well combined, but do not overmix.
Combine the salmon mixture and breadcrumbs until well combined.
Evenly divide the salmon mixture into 4 patties. Grill for 4 minutes on each side or until fully cooked through.
Serve on a bun with lettuce, tomatoes, onions, and mayo, if desired.