Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil and lightly grease the aluminum foil.
Whisk miso paste, water, mirin, sake, and brown sugar together in a small skillet over medium heat until mixture simmers and thickens slightly, 1 to 3 minutes. Remove from heat and cool completely.
Place cod fillets on prepared baking sheet. Brush fillets all over with miso mixture. Rest fillets at room temperature to quickly marinate, 15 to 20.
Broil fillets in the preheated oven for 5 minutes. Turn the baking sheet 180 degrees and continue broiling until fish flakes easily with a fork, about 5 minutes more. Remove pin bones.
