In a large mixing bowl, toss sweet potato, carrots, rutabaga, parsnips, Brussels sprouts, and garlic with olive oil and balsamic vinegar. Season with garlic powder and salt and pepper, to taste.
Divide the vegetables onto two large rimmed baking sheets in a single layer. Place one sheet on the top oven rack and the other sheet on the bottom rack. Roast for 25 minutes, moving the top tray to the bottom and the bottom to the top halfway through.
Remove from oven and stir in beans. Roast until beans are slightly crisped and veggies are golden, softened, and crispy, about 5 minutes more. Turn on the broiler for another 2-3 minutes to crisp up the veggies, watching closely so they don't burn.
Serve immediately. Store leftovers in the fridge for up to 3 to 4 days, if they'll last that long!