Preheat an outdoor grill to medium heat.
Stir together the rice vinegar and 1/4 cup of the Japanese Style Teriyaki Cooking Sauce in a medium bowl.
Oil the grill grates. Brush the salmon and scallions with oil. Sprinkle with salt and pepper. Place the salmon on the grill, flat-side down, and brush the tops with some of the remaining cooking sauce. Place the scallions on the grill and brush with some of the remaining cooking sauce. Cover and cook until the scallions are charred and tender, about 3 minutes. Flip the fish, brush with the remaining cooking sauce and continue to cook until the fish is almost cooked through (it will cook more after you remove it from the grill), 4 to 5 minutes per side. Remove the salmon and scallions to a cutting board. Coarsely chop the scallions.
Add the cucumber, avocado and scallions to the bowl with the vinegar sauce and toss. Mound the salad onto 4 serving plates. Plate the salmon next to the salad. Sprinkle with the sesame seeds.
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