Bring the sake and mirin to a boil in a medium saucepan over high heat for 20 seconds to evaporate the alcohol. Turn the heat down to low, add the miso paste, and whisk. When the miso has dissolved completely, turn the heat up to high again and add the sugar, whisking constantly to ensure that the sugar doesn’t burn on the bottom of the pan. Remove from heat once the sugar is fully dissolved. Cool to room temperature.
Pat the black cod fillets thoroughly dry with paper towels. Place the fish and the miso marinade in a resealable plastic bag. Leave it flat on a plate and let it marinate overnight (or 2 to 3 days).
Lightly wipe off the marinade from the fillets.
Heat oil on a non-stick skillet over high heat. Place fish skin side up on the pan and cook until the bottom of the fish browns and blackens in spots, about 3 minutes. Flip and continue cooking until the other side is browned, 2 to 3 minutes. The fish is ready when it’s opaque and flakes easily.