Preheat the broiler. On a foil-lined rimmed baking sheet, arrange the cod. Season with salt and pepper.
Into a small bowl, zest the orange and lime. Add the brown sugar, oil, soy sauce, and cumin. Stir together and brush all over cod. Broil cod 7–8 min., until cooked through.
Meanwhile, add the broccoli and ¼ cup water to a microwave-safe bowl. Cover with vented plastic and microwave 2–3 min., until stems are tender. Drain. Squeeze juice of lime and orange over broccoli. Season with salt to taste. Serve cod with broccoli.