Roasted duck takes time to cook. The body of meat is surrounded by a thick layer of fat that renders out during the roasting process. If you want to add vegetables to the oven during the roasting process, they need to be the type that withstands long and slow heat. Otherwise, you can choose to add them towards the end of the roasting time, cook vegetables separately to serve with the roasted duck or simply serve raw vegetables.
Long and slow roasted vegetables like onions and cabbage as well as several root vegetables like turnips, parsnips, beets and carrots tend to cook well, turning sweet with the long heat. You should cook them in a covered container, or they will dry out and burn during the six hours or so it takes to roast a duck. You can try to situate the vegetables under the duck so they stay covered during the cooking process and take on the flavor of the duck. Once you remove the duck from the oven and slice it up on a platter, you can arrange the roasted vegetables around the meat.
You can roast faster cooking vegetables like potatoes, winter squash or yams during the last hour of cooking. Place them in a baking pan and drizzle some of the duck drippings over them to flavor them. Toss whole baby carrots or fingerling potatoes, golden beets or baby squashes, garlic cloves or shallots around the roast duck to cook in the same heat.
Sauté or steam fresh vegetables on the stove top to contrast with the heaviness of the roast duck. Green beans, snow peas, zucchini, baby carrots and broccoli cook quickly and will complement the meat. Do not add any extra butter to the pan as the duck will have enough fat for each serving. Add a side of soft mashed potatoes for a traditional meal.
Serve the duck on a bed of fresh greens like baby spinach, arugula, dandelion greens or any combination tossed in balsamic vinaigrette mixed with chopped raisins and thinly sliced red onions. The depth of the roasted duck flavor should contrast nicely with the piquancy of the vinegar and onions and the tender crunch of the greens against the soft duck meat.