Preheat the oven to 400°F (200°C) and line a baking pan with parchment paper.
Trim the butt end of the Brussels sprouts and cut them in half lengthwise. Make sure not to cut more than just shaving off the most calloused-looking part of the butt end of the Brussels sprouts so that they don’t fully fall apart when tossed.
Either roll-cut the carrots or quarter them and slice them into 2-inch (5 cm) long sections, aiming for even thickness to ensure they roast uniformly.
In a large mixing bowl, toss the Brussels sprouts and carrots with olive oil until well-coated. Spread the vegetables evenly on the prepared baking pan. If using thyme, place the sprigs among the vegetables.
Roast for 15 minutes at 400°F (200°C).
While the vegetables roast, in a small bowl, whisk together the maple syrup, balsamic vinegar, and grated ginger.
After the vegetables have baked for 15 minutes, remove them from the oven and drizzle the maple balsamic over the partially roasted vegetables.
Return the vegetables to the oven and roast for an additional 15-20 minutes, or until the Brussels sprouts are golden and the carrots are tender.
Once out of the oven, sprinkle with black pepper and salt. Transfer the vegetables to a serving dish. Garnish with sliced scallions or fresh parsley, if desired.