Chop the salmon filet into small pieces (about 1/4 inch) and transfer it into a medium mixing bowl.
Gently stir in bread crumbs, cilantro, egg, mayonnaise, lemon juice, mustard, 1/2 tsp salt and 1/2 tsp pepper. Let the mixture rest for 5-10 minutes.
Heat a little 1 tbsp oil in a large non-stick grill pan over medium heat. Divide the salmon mixture into 6 and form neat patties. Fry/grill the patties until browned on both sides and just cooked through; about 4 minutes on each side.
For the salsa:
Combine remaining ingredients together and mix well. Garnish patties with a spoonful of salsa.