In a small saucepan, whisk together the ¼ cup soy sauce, ¼ cup mirin, 2 tbsp sake, and 2 tbsp brown sugar. Add the 1 tsp fresh ginger finely grated and 1 clove garlic finely grated or minced if using. In a separate small mixing bowl, stir the 1 tsp cornstarch into the 1 tbsp cold water until fully dissolved, then set aside.

Place the saucepan over medium heat and bring to a gentle simmer, stirring occasionally, until the sugar dissolves — about 2 minutes. Stir in the 1 tsp cornstarch slurry and continue to cook, stirring constantly, for 1–2 minutes until the sauce thickens slightly and coats the back of a spoon. Remove from heat and set aside.

Pat fillets thoroughly dry with paper towels — moisture kills your sear. Season both sides generously with kosher salt and black pepper; drizzle olive oil on the fish or add it to the pan. Let fillets rest at room temperature while the skillet heats. Check the flesh for pin bones and pull any out with tweezers. Keep a fish spatula close for pressing and flipping.

Heat a cast iron or stainless steel skillet over medium-high for 2–3 minutes until nearly smoking. Add high-heat oil and let it shimmer. Lay fillets skin-side down, pressing gently with a spatula for the first 30 seconds to prevent curling. Do not move them. Cook skin-side down 4–5 minutes until skin is crispy and flesh is opaque two-thirds up the side. Flip, reduce to medium, cook 1–2 minutes more. Total time: 8–12 minutes depending on thickness. For thick fillets, sear each side 2 minutes on the stovetop, then finish in a 350°F oven for 4–5 minutes.

Transfer the 4 salmon fillets skin-on to plates or a serving platter. Drizzle any remaining pan sauce over the top. Garnish with sliced stalks green onions thinly sliced and toasted 1 tsp sesame seeds toasted. Serve immediately with steamed rice and vegetables.

Pour the teriyaki sauce over the salmon fillets in the pan. Spoon and baste the sauce over the fillets as it bubbles and reduces, about 1–2 minutes. The sauce will caramelize and cling to the fish. Watch closely — the sugars can burn quickly. Remove from heat when the salmon fillets reaches an internal temperature of 125–130°F for medium, or 145°F for well done.

Transfer the salmon fillets to plates or a serving platter. Drizzle any remaining pan sauce over the top. Garnish with sliced green onions and toasted sesame seeds. Serve immediately with steamed rice and vegetables.