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Heat the grill to high and brush a sturdy baking tray with oil. In a large bowl, mix the soy, mirin, sugar, ginger and garlic together until the sugar has dissolved, then toss the frozen salmon in the soy mix until coated. Tip the remaining marinade into a small saucepan and bring to a simmer.
Place the tray about 4in away from the heat, then grill for 20 mins. Brush the fish every few mins with the simmering marinade until cooked through and glazed. If the fillets are thick, you may need to turn them on their sides so they cook evenly. Remove from the grill. Simmer the marinade until sticky, then pour it over the cooked salmon.
For the cucumber salad, use a swivel blade peeler to peel the cucumber into slices. Make the dressing by mixing the vinegar with the soy sauce, sugar and sesame seeds. Toss the cucumber with the dressing and serve with the salmon and boiled rice.