Pat yellowtail fillets dry with paper towels. Sprinkle salt evenly on both sides. Let stand for 10 minutes, then pat dry again to remove excess moisture.
In a small bowl, combine soy sauce, mirin, sake (for sauce), and sugar to make the teriyaki sauce. Mix well until sugar is dissolved.
Heat vegetable oil in a non-stick pan over medium-high heat. Place the yellowtail fillets skin-side down (if applicable) in the pan. Cook for 3-4 minutes until the skin is crispy and golden.
Flip the yellowtail fillets and cook for another 3-4 minutes on the other side until cooked through.
Reduce the heat to medium-low. Pour the teriyaki sauce into the pan. Bring to a simmer, spooning the sauce over the fish fillets repeatedly until the sauce thickens and coats the fish evenly. This takes about 2-3 minutes.
Remove the buri teriyaki from the pan and place on serving plates. Drizzle any remaining sauce over the fish.
Garnish with white sesame seeds, shredded nori, and thinly sliced green onion if desired. Serve immediately with rice.
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