Preheat oven to 425 degrees F (220 degrees C). Set an oven rack to the second-lowest level in the oven.
Fill a bowl with lightly salted water. Place Brussels sprouts in salted water and let sit for about 15 minutes; drain.
Stir potatoes, carrots, cauliflower, beets, shallot, olive oil, salt, and pepper together in a bowl. Pour vegetables in a single layer onto a baking sheet.
Roast in the preheated oven until caramelized and cooked through, about 45 minutes.