Preheat the oven to 400°F (200°C).
In a large bowl, toss Brussels sprouts and carrots with olive oil, salt, and pepper.
Spread the vegetables out in an even layer on a large baking sheet.
Roast in the preheated oven for 20 minutes.
While the vegetables are roasting, mix balsamic vinegar and honey in a small bowl.
After 20 minutes, remove the baking sheet from the oven, drizzle the balsamic honey mixture over the vegetables, and toss to coat.
Return to the oven and roast for an additional 10 minutes, or until the vegetables are tender and caramelized.
Serve immediately and enjoy!