Mix the Marinade: Combine the brown sugar, teriyaki sauce, hoisin sauce, soy sauce, vinegar, sesame oil, garlic, and ginger in a medium-sized bowl. Stir until the sugar fully dissolves, creating a smooth mixture.
Marinate the Salmon: Place the salmon fillets in a large zip-top bag. Pour half of the prepared marinade into the bag, ensuring the salmon is evenly coated. Carefully remove excess air from the bag, seal it tightly, and massage the marinade into the salmon. Place the bag in the refrigerator to marinate for at least 30 minutes, or up to 1 hour. Store the remaining marinade in a sealed container in the refrigerator.
Prepare for Baking: Preheat the oven to 400°F. Line a large rimmed baking sheet with foil for easy cleanup.
Bake the Salmon: Remove the salmon from the marinade, discarding the liquid in the bag. Arrange the salmon pieces on the prepared baking sheet, skin side down. Bake for 12 to 16 minutes, depending on the thickness of the salmon, until the fish is flaky and an instant-read thermometer inserted into the thickest part reads 145°F.
Cook the Sauce: Heat the reserved marinade in a small saucepan over medium heat. Bring it to a simmer and cook for 3 to 4 minutes, stirring occasionally, until it thickens slightly. Remove from heat.
Glaze and Garnish: Once the salmon is done baking, brush the thickened marinade over the fillets for a shiny, flavorful glaze. Sprinkle with sliced green onions and sesame seeds before serving.