Heat oven to 450 degrees. Place the vegetables on two edged baking sheets.
In a medium bowl, whisk together the brown sugar, oil (or stock) 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 10-15 minutes, toss to coat well, and finish roasting. Season to taste with sea salt and freshly ground pepper.