Make the pickle: In a heatproof bowl, stir together the bell pepper and ginger. In a small saucepan, heat the oil over medium-high heat. When the pan is hot, add the garlic and stir until lightly golden, about 1 minute. Add the vinegar, mirin, and 2 tablespoons water and bring to a boil. Pour the boiling liquid over the red pepper and ginger and let sit at room temperature for at least 20 minutes and up to 1 hour.

Make the spice rub: In a small bowl, mix the spice rub ingredients. Use your fingertips to blend the zest well with the spices.

Sear-roast the fish: Coat all sides of the halibut fillets with the rub and set on a plate. Heat the oil in a heavy 12-inch ovenproof skillet over medium-high heat. When the oil is shimmering hot, arrange the halibut fillets evenly in the pan, skinned side up. Sear for about 2 minutes, without moving; then use a slotted metal spatula to lift a piece of fish and check the color. (Note: watch carefully so the sugar in the rub doesn't burn. If necessary, reduce the heat.) When the fillets are nicely browned, flip them and put the pan in the oven.

Roast until the halibut is just cooked in the middle, 5 to 6 minutes. (If your fillets are thick, check again that the sugar in the rub does not burn while the fish is in the oven. You can turn the fish on one or both edges to avoid burning the rub.) Remove the pan from the oven and transfer the halibut to serving plates.

Drain the pickled red pepper and ginger, discarding the liquid, and toss with the scallion and sesame oil in a small bowl. Top each portion of halibut with some of the pickle and serve.