Combine the mirin, soy sauce, sugar, ginger, garlic, and cayenne in a small saucepan and bring to a boil. Lower heat and simmer until reduced a thick glaze, 5 to 6 minutes. Remove from the heat. Set aside 1/4 cup of the teriyaki sauce.

Set the halibut fillets in a baking dish and sprinkle with cayenne and add the remaining teriyaki sauce. Marinate for 15 minutes and up to 1 hour.

Place the sesame seeds in a dish and dip the fillets onto the seeds, pressing lightly to coat each side with about 1 teaspoon of seeds.

Heat the oil in a large skillet over medium-high heat. Add the fillets and cook until browned and just done, 3 to 4 minutes per side. Remove from the pan to 4 serving plates. Garnish with the green onions and  remaining glaze. Serve with the Cucumber Noodles.