In a marge bowl, whisk together soy sauce, brown sugar, hoisin sauce, rice wine vinegar, garlic, and ginger.
Pour half of the teriyaki sauce into a shallow container or zip lock. Add the salmon fillets, cover or seal, and marinate in the refrigerator for at least 1 hour.
Just before taking out the salmon fillets from the marinade, pour the remaining teriyaki sauce into a small saucepan and bring to a boil. One boiling, lower heat to simmer for about 20 minutes to thicken the sauce.
Meanwhile, heat an outdoor grill or indoor grill pan to medium heat. Brush with extra virgin olive oil.
Add the salmon fillets and grill for about 6 minutes on each side.
Just before serving, brush each fillet with the thickened reserve teriyaki sauce. Sprinkle sesame seeds and sliced green onions, and serve immediately.