Preheat oven to 425.
Peel (if necessary) and chop the vegetables into bite-sized pieces. Place them on a large rimmed baking sheet. If roasting more than one type of vegetable, pair similar vegetables together to ensure even cooking (potatoes/sweet potatoes with carrots; broccoli with cauliflower or Brussels sprouts).
Drizzle 1 tablespoon olive oil over the vegetables, and gently toss to coat. Add additional oil if needed. Sprinkle with salt and pepper. Spread the vegetables into a single layer to cook evenly.
Roast the vegetables until tender and slightly charred. (Softer vegetables, such as cauliflower, will cook in approximately 12-15 minutes, while hard vegetables, such as winter squash or potatoes, will take 30-40 minutes, depending on the size of the pieces.)