Preheat the 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. Arrange vegetables in a single layer on a baking sheet.

Roast in the preheated oven until caramelized and cooked through, about 45 minutes.