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 the oven to 400°F.
Heat a nonstick grill pan over high; lightly grease pan with oil.
Remove fillets from marinade; scrape off excess marinade. Discard marinade.
Working in batches, if needed, add fillets, skin side up, to pan; cook, undisturbed, over high until browned, 1 to 2 minutes.
Transfer fillets, browned sides up, to a parchment paper–lined rimmed baking sheet.
Roast in preheated oven until flaky and cooked through, 8 to 10 minutes.
Transfer fillets, skin side down, to plates. Serve with pickled ginger, if desired.
