Preheat oven to broil with rack about 7 inches from heat. Whisk together soy sauce, sugar, mirin, vinegar, sesame seeds, and ginger in a small bowl.
Place salmon in a large ziplock plastic bag, and pour in teriyaki sauce. Seal bag, and turn to evenly coat fish. Marinate at room temperature 15 to 30 minutes.
Toss together green beans, sesame oil, salt, and granulated garlic on a large rimmed baking sheet. Broil until beans are just softened, about 3 minutes.
Remove baking sheet from oven; stir beans, and spread into a single layer. Place a broiler-safe wire rack inside baking sheet over beans. Transfer salmon, skin side down, to wire rack, shaking excess teriyaki sauce back into bag; reserve teriyaki sauce. Return baking sheet to oven, and broil until salmon is opaque and starting to brown in spots, about 5 minutes. Meanwhile, bring reserved teriyaki sauce to a boil in a medium skillet over high. Cook, stirring occasionally, until reduced to about 1/2 cup, 3 to 4 minutes.
Brush tops and sides of salmon fillets with 1/4 cup teriyaki glaze; set remaining glaze aside. Continue broiling until salmon is glossy and flakes with a fork and beans are tender, 2 to 3 minutes.
Serve salmon and beans with rice, if desired; drizzle with remaining glaze, and garnish with scallions.