Preheat your oven to 400°F (200°C). In a large mixing bowl, combine sliced carrots, halved Brussels sprouts, and cubed sweet potatoes. Drizzle with olive oil, then toss together until the vegetables are evenly coated. Season with salt and pepper to taste.
Spread the vegetables evenly on a baking sheet in a single layer, ensuring they aren’t crowded. Place in the oven and roast for about 25-30 minutes, until the edges are golden and caramelized, and the vegetables are tender when pierced with a fork.
While the vegetables roast, prepare the balsamic glaze by pouring the balsamic vinegar into a small saucepan. Bring to a gentle simmer over medium heat and cook until it thickens and reduces by half, about 8-10 minutes. Add honey or maple syrup if desired for extra gloss and sweetness.
Once the vegetables are roasted, remove the baking sheet from the oven and drizzle the balsamic glaze over the warm vegetables. Toss gently to coat each piece evenly, allowing the glaze to cling and slightly caramelize from the residual heat.
Transfer the glazed vegetables to a serving platter. Let them rest for a minute so the flavors meld and the glaze sets slightly, creating a shiny, sticky finish.
Serve warm, enjoy the vibrant colors and the combination of crispy exterior with tender, caramelized interiors. These vegetables make a flavorful side or a hearty vegetarian main dish.