Place chopped salmon in a food processor with onions, bell pepper, and garlic.
Pulse the salmon a couple of times and scrape down the sides as needed until the salmon is coarsely ground.
Add the rest of the burger ingredients - egg, parsley, breadcrumbs, Cajun seasoning, salt, and pepper. Pulse until thoroughly combined.
For easier handling, cover and refrigerate the salmon mixture for at least an hour or more until firm.
Divide the salmon mixture into four equally-sized balls and form into slightly flattened, round patties. Place on a plate and chill in the refrigerator until ready to use.
Thoroughly clean grates with a grill brush and olive oil, then preheat on medium-high.
Once hot, add salmon patties and cover. Cook until brown and slightly charred on one side, about 4-5 minutes.
Flip and cook an additional 4-6 minutes or to the desired doneness.
Do not overcook them, as it will result in a dry burger. You can also use a meat thermometer (145℉/63℃) to check for the desired doneness.
Remove and place on a plate, tent with foil, and let rest for 5 minutes.
Lightly toast the burger buns, if desired.
Assemble salmon burger by spreading buns with garlic aioli and topping with spinach and arugula, grilled patties, tomatoes, and onions.
Enjoy!