Preheat your oven to 375°F (190°C) and lightly grease a baking dish.
In a small saucepan, combine the soy sauce, mirin, honey or brown sugar, rice vinegar, minced garlic, and grated ginger. If you prefer a thicker sauce, mix the cornstarch with a tablespoon of water and add it to the sauce mixture. Stir well to combine.
Place the saucepan over medium heat and bring the mixture to a simmer. Cook for about 5 minutes, stirring occasionally, until the sauce thickens slightly. Remove from heat and set aside.
Arrange the salmon fillets in the greased baking dish, skin-side down. Pour half of the teriyaki sauce over the salmon, reserving the other half for later.
Bake the salmon in the preheated oven for about 15-20 minutes, or until the salmon is cooked through and flakes easily with a fork. The cooking time may vary depending on the thickness of your fillets.
Once the salmon is cooked, remove it from the oven and brush the remaining teriyaki sauce over the top.
If desired, sprinkle some sesame seeds and chopped green onions over the salmon for garnish.
Serve the baked teriyaki salmon with steamed rice or your favorite side dishes. You can drizzle some extra teriyaki sauce over the salmon if you like.