In a large food processor, pulse together all ingredients except the parsley and scallions. Mix until all ingredients are thoroughly combined and the salmon achieves a pureed texture.
Transfer the salmon burger mix into a large bowl and stir in the scallions and parsley to combine.
Working with clean hands, form the burger mix into patties about 2" wide and 1" thick. Adjust the size based on your liking. Place on a clean plate.
Whether using a grill or grill pan, cook the burgers on medium hot heat for 3-4 minutes each side. The internal temperature should reach at least 145 degrees Farenheit.