Set the oven to 425 °F. Spray nonstick cooking spray on a baking pan. Add salt and pepper to the prepared dish before adding the fish.

In the meantime, heat a small saucepan over medium heat and bring lime juice, vinegar, soy sauce, brown sugar, and a bit of salt to a boil. Simmer until thick and syrupy, about 4 to 5 minutes. Each cod filet should have a teaspoon of glaze evenly spread over it; save the extra.

Bake the baking dish for 12 minutes, or until it is opaque and barely cooked through. Serve with the reserved glaze with mint and scallions on the side.