Prepare 1 large red onion, 3 carrots, 12 brussels sprouts, 1 large sweet potato, 4 medium potatoes, and lay them out in a single layer on a large rimmed baking sheet.
Make the dressing
Combine 1/4 cup olive oil, 2 tablespoons balsamic vinegar, 2 tablespoons dark brown sugar, and salt and pepper in a bowl. Reserve a tablespoon or 2 for later.
Pour over vegetables, and using your hands, mix it so all of the vegetables are covered evenly.
Bake
Bake for 30-45 minutes (or until your vegetables are tender, and brown).
Cool, then drizzle with the reserved vinaigrette, and sprinkle with 1/4 cup feta cheese.