Put vegetables into ovenproof baking dish, large enough to allow one layer. Pour olive oil and honey over the vegetables, and toss well. Snip as much of the rosemary off the stems as you can, and tuck the stems among the vegetables. Season well with salt and pepper.
Roast at 375 until potatoes and parsnips are tender, and broccoli begins to caramelize, about 25 minutes.