Cut salmon into small pieces. In a blender or food processor, pulse in batches for about 10 to 15 seconds each, until coarsely ground. In a mixing bowl mix together ground salmon, heavy cream, cornstarch, shallots, chives, parsley, salt, and white pepper until well blended.
Shape salmon mixture into six 1/2-inch thick patties. Place patties on waxed paper. Spray with non-stick cooking spray and place in refrigerator for 5 minutes.
Place patties, sprayed side down, in centre of cooking grate. Grill 6 to 8 minutes or until well-done, turning once halfway through grilling time. Place each patty on a bun; top with one slice of smoked cheese and 1 tablespoon of pickle relish.