Heat broiler. In a small bowl, combine the brown sugar, soy sauce, and ginger. Set aside.
Place the fish on a foil-lined broilerproof rimmed baking sheet. Drizzle with 1 teaspoon of the oil and season with ¼ teaspoon each salt and pepper.
Broil until the fish is opaque throughout, 5 to 7 minutes. Baste with the soy mixture twice during the last 2 minutes of cooking.
Meanwhile, heat the remaining 2 tablespoons of the oil in a large skillet over medium-high heat.
Add the zucchini and squash, crushed red pepper, and ½ teaspoon salt. Cook, tossing frequently, until just tender, 5 to 7 minutes. Fold in the mint.
Serve the vegetables with the fish.