Bring mirin and sake to a boil in a small saucepan over medium. Whisk in miso until thoroughly combined, about 1 minute. Add sugar; cook over medium, whisking constantly, until sugar dissolves, 1 to 2 minutes. Transfer marinade to a 9- x 13-inch baking dish; let cool completely, about 20 minutes. Add fillets to marinade, turning to coat. Cover and refrigerate at least 8 hours or up to 48 hours.

Preheat oven to broil with oven rack positioned 6 to 8 inches from heat. Heat oil in a large ovenproof skillet over high. Remove fillets from marinade; scrape off excess marinade. Discard marinade. Place fillets, skin side up, in skillet; cook over high, undisturbed, until flesh is browned, 2 to 3 minutes. Flip fillets. Transfer skillet to preheated oven and broil until cod is flaky and cooked through, 4 to 6 minutes, watching fillets carefully to ensure they do not scorch. Transfer fillets, skin side down, to plates. Serve with pickled ginger, if desired.