• Freshly ground black pepper, to taste
Preheat oven to 375 degrees. Using a sharp knife, score the flat sides of the chestnuts with an X. Scatter over a baking sheet and roast until the shell peels back, about 8 to 10 minutes. Remove and wrap the chestnuts in a heavy dish towel to steam while they cool. Then, peel away the leathery shells.
While the chestnuts are cooling, halve the larger Brussels sprouts and toss them all with about 2 tablespoons of olive oil to coat. Scatter on a baking sheet, sprinkle with coarse salt and roast, shaking the pan occasionally, until they become tender and turn brown at the edges, about 10 minutes.
In a small bowl, whisk together the remaining 2 tablespoons of oil with the balsamic vinegar and syrup.
Toss the prepared chestnuts onto the pan with the roasted Brussels sprouts, drizzle the oil-balsamic mixture over all and toss to coat. Return to the oven to glaze, about 3 minutes. Season with the ground pepper. Serve hot or at room temperature.