In a medium-size bowl, combine the grapes, brown sugar, balsamic vinegar, cinnamon, and nutmeg. Toss gently to coat. Let stand at room temperature 30 minutes, tossing occasionally.

Meanwhile, thoroughly wash the carrots; trim off the ends. Peel or scrub the carrots. Cut the carrots into thin 2-1/2-inch-long sticks. (To make the thin sticks, cut the carrots into thirds crosswise, then in half lengthwise. Continue cutting the carrots lengthwise to create long, thin sticks.)

To steam the carrots, place a steamer basket in a Dutch oven. Add water to just below the basket. Bring the water to a boil over high heat. Place the carrot sticks in the steamer basket. Cover and steam 6 to 8 minutes or until the carrots are crisp-tender. Remove from heat.

Drain the grapes, reserving the liquid. In a small bowl, stir together the reserved grape liquid, the Grand Marnier or brandy, and cornstarch.

In a large skillet, melt the butter over medium heat. Add the grapes, tossing gently to coat with the butter. Stir the cornstarch mixture into the grapes in the skillet. Cook, stirring constantly, until the mixture thickens. Stir in the carrots. Cook, stirring constantly, 1 to 2 minutes or until the grapes are heated through.

To serve, transfer the carrot mixture to a serving bowl. Sprinkle with the parsley.