Position rack in upper third of oven and preheat to 425°F. Mix brown sugar, cumin, salt, pepper, and cayenne in a small bowl. Toss squash, fennel, and grapes with oil and half of spice mixture on rimmed baking sheet and arrange in a single layer.
Rub chicken thighs with remaining spice mixture and arrange, skin side up, on top of fruit and vegetables. Roast until skin is browned and an instant-read thermometer inserted into the thickest part of chicken registers 165°F, about 35 minutes; if chicken skin or vegetables start to burn, move pan to a lower rack to finish cooking.
Divide chicken, fruit, and vegetables among 4 plates and top with mint.
