The roasting process brings out the natural sweetness and earthy flavors of this medley of Fall and Winter vegetables.
Position the rack in the center of the oven and preheat to 425 F.
In a large rimmed baking sheet, toss the brussels sprouts, parsnips, and carrots, with 3 tablespoons oil. Arrange the vegetables to form a single layer.
Sprinkle with the thyme, salt, and pepper.
Add the 1/4 cup of water and bake stirring occasionally until tender, about 45 minutes.
Transfer to a serving platter and sprinkle some fresh thyme springs on the vegetables. Serve warm or at room temperature.
Make Ahead: The brussels sprouts can be trimmed and halved and the carrots and parsnips can be peeled and cut one day in advance. Store in an airtight container or a bag with zip closure and refrigerate until ready to use.