Add salmon, egg, breadcrumbs, 1 tbsp (15 mL) mayonnaise and soy sauce to food processor; pulse just until finely chopped. Transfer to bowl. Stir in green onions. Divide into 4 portions. Form into ¾-in. (2-cm) thick patties. Cover and chill 10 min., or up to 1 day, to firm up.
Meanwhile, in small bowl, stir remaining mayonnaise with pickled ginger and wasabi. Set aside. Brush chilled patties with oil and place on grill preheated to medium-high. Cook 5 to 6 min. per side ,or until instant-read thermometer inserted through side into centre reads 158°F (70°C).
Grill split buns 1 to 2 min. per side, until lightly toasted. To arrange open-face burgers, plate bun halves cut-sides up; top with cucumber slices, patties, ginger-wasabi mayonnaise and sesame seeds.
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