In a medium bowl, add the soy sauce brown sugar, garlic, ginger, rice vinegar, and sesame oil, and whisk to combine.
Add the salmon to a baking dish and cover with all but ½ cup of the marinade.
Cover and refrigerate for at least 30 minutes, up to 8 hours.
Reserve the remaining sauce in a smaller container in the fridge.
Preheat your grill to 350 degrees, about medium heat.
Grease your grill thoroughly.
Add the marinated salmon, skin side up, and close the grill.
Cook the salmon for 8 minutes and then flip over. Brush with additional marinade. Close the grill and cook for another 4-6 minutes, until it is cooked through and easily flakes. Use a meat thermometer to ensure the salmon is cooked to 120-125 degrees F in the thickest part.
Serve topped with the reserved teriyaki sauce, chopped green onions, and white sesame seeds.
Enjoy!