In a small bowl, whisk together soy sauce, brown sugar, rice vinegar, sesame oil, garlic, and ginger.
Place salmon fillets in a shallow dish and pour the marinade over them.
Cover and refrigerate for at least 30 minutes.
Preheat your grill or oven to medium-high heat.
Remove salmon from marinade and let excess liquid drip off.
Grill salmon for 5-7 minutes on each side, or until cooked through.
In a saucepan, bring the marinade to a boil and reduce for about 5 minutes.
Brush the thickened marinade over the salmon during the last minute of cooking.
Garnish with sesame seeds and sliced green onions before serving.