This dish can be served warm or at room temperature.
Preheat oven to 450 degrees. On a rimmed baking sheet, toss halved brussels sprouts with oil; season with salt. Spread in a single layer and roast, stirring once halfway through, until browned and crisp in places, 35 to 40 minutes.
Meanwhile, combine cider, vinegar, and Dijon in a saucepan; season with salt and pepper. Boil, stirring occasionally, until syrupy and reduced to 1/4 cup, about 12 minutes.
Toss roasted and raw brussels sprouts with chestnuts, cider reduction, and 1/4 cup pomegranate seeds; season with salt and pepper. Top with remaining 1/4 cup pomegranate seeds; serve.