Pulse salmon pieces in food processor until it reaches small-chop consistency. In a bowl, mix salmon with mayonnaise, grated shallot, garlic, ginger, sesame oil, soy sauce, salt and pepper. Cover and chill for at least one hour. Form mixture into patties; refrigerate covered for an additional hour. The burgers will be quite soft, but once they are coated in flour, they are very manageable.
To cook, carefully dredge burgers in flour. Cook patties in a nonstick skillet over medium-high heat for 3-4 minutes per side, or until golden brown, turning only once, if possible. Serve on buns, or over a bed of mixed greens. 4 servings.