Heat oven to 450° F. Place the vegetables in two small roasting pans.
In a medium bowl, whisk together the brown sugar, oil, and vinegar. Pour over the vegetables and toss to coat well.
Cook until tender, about 1 hour, stirring halfway. Add the mushrooms during the last 10 minutes, toss to coat well, and finish roasting. Season to taste with salt and freshly ground pepper.