In a mixing bowl, whisk together the soy sauce, mirin, brown sugar, rice vinegar, minced garlic, and grated ginger to create the teriyaki sauce.
Place the salmon fillets in a shallow dish or a resealable plastic bag.
Pour half of the teriyaki sauce over the salmon, reserving the other half for later.
Marinate the salmon in the teriyaki sauce for at least 10 minutes to allow the flavors to infuse into the fish. For even more flavor, you can marinate the salmon for up to 30 minutes in the refrigerator.
Heat vegetable oil in a skillet or grill pan over medium-high heat.
Remove the salmon from the marinade, shaking off any excess sauce, and place the fillets in the hot skillet, skin-side down (if using skin-on salmon).
Cook the salmon for about 3-4 minutes on each side, depending on the thickness of the fillets, until it develops a beautiful golden-brown caramelized crust and is cooked to your desired level of doneness.
While the salmon is cooking, take the reserved teriyaki sauce and heat it in a small saucepan over medium heat until it thickens slightly and reduces to a glaze consistency.
Once the salmon is cooked, remove it from the skillet, and place it on a serving plate.
Drizzle the reduced teriyaki glaze over the salmon.
Optionally, garnish the Teriyaki Salmon with sesame seeds and sliced green onions for added texture and visual appeal.
Serve the Teriyaki Salmon hot with a side of cooked rice or steamed vegetables, and enjoy the delightful flavors of this Japanese-inspired dish!