Remove the skin from the salmon or have your fishmonger do it for you. Check the fillet over for pin bones and remove any you find with tweezers or needle-nose pliers. Cut the salmon into 2-inch chunks. Put the salmon, scallions, garlic, ginger, tamari, and sesame oil in the bowl of a food processor. Pulse until combined. This may take 5 to 6 pulses, but do not let the machine run. Pour this mixture into a medium bowl and add the breadcrumbs and sesame seeds. Use your hands to gently combine.
Divide the salmon mixture into 4 equal portions and shape into patties about 3/4 inch thick. Remember to put a slight indentation into the center of each patty. Season both sides of the burgers liberally with salt and pepper. Refrigerate for at least 1 hour. This will help the burgers hold together on the grill.
Oil the grill racks well, and make sure that they are impeccably clean. Preheat your grill using all burners set on high and with the lid closed for 10 to 12 minutes.
Remove the burgers from the refrigerator and spray both sides of each with the cooking spray. Place on the grill and cook for 5 minutes. Turn and cook for 4 minutes longer, so the burgers are just cooked through. Use a spatula to turn your burgers, but loosen them from the grill before you make the attempt. During the last minute or two, place the buns on the grill, cut side down, so they get warm and toasty. Remove all from the grill to a platter, and top with lettuce and either the peanut sauce or the sweet chili sauce.