Cook potatoes in a large pot with water to cover 20 to 25 minutes until tender when pierced. Drain in a colander. Gradually beat in milk, butter, salt and pepper until blended. Cook in water to cover 20 to 25 minutes until tender. Roast after stuffing has come out of the oven.
Position racks to divide oven in thirds.
Trim broccoli, leaving 2-in. Cut into florets. Peel and slice onion. Divide vegetables between prepared baking sheets. Drizzle with oil, sprinkle with salt and pepper, then toss to coat.