Working quickly to keep as cold as possible, cut the salmon into 1″ chunks. Take about a quarter of the salmon and add to a food processor along with the mustard. Process until the mixture becomes a paste, stopping to scrape down sides.
Add the remaining salmon and pulse off and on until the salmon is chopped into fine pieces. Don’t over process into a paste but make sure there are no large chunks. Remove to a bowl.
By hand, stir in egg, breadcrumbs (start with half a cup, add more after you’ve added the rest of the ingredients if the burgers seem very wet) green onions, peppers, garlic, lemon juice, soy sauce, salt, and pepper.
Shape into four burgers. If desired, burgers may be refrigerated at this point. (I find the burgers hold together better if they spend some time in the refrigerator, 30 minutes to four hours.)
If grilling, brush the patties with butter or oil and grill about 4 minutes the first side (don’t turn too soon or they won’t be firm enough to remove from the grate) then turn and finish for a moment or two.
If using a pan, place butter or oil in a nonstick skillet and heat to medium-high. When the foam subsides or oil is hot, cook burgers for two to three minutes per side, turning once.
Doneness can be checked by making a small cut with a knife, but be careful not to overcook it.
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