In a large bowl, combine the chopped salmon, breadcrumbs, mustard, garlic, red onion, parsley, paprika, salt, and pepper.
Use clean hands or a spoon to gently mix the ingredients until just combined—don’t overwork it.
Form the mixture into 4 equal-sized patties. If they’re a bit soft, refrigerate for 10 minutes to firm them up.
Heat olive oil in a grill pan or on an outdoor grill over medium heat.
Grill the patties for about 4 minutes per side, or until fully cooked and lightly charred.
Meanwhile, toss together the avocado, cherry tomatoes, lime juice, salt, and pepper to make the salsa.
Toast the buns if desired. Place a patty on each bun, top with avocado salsa, and serve warm.