Preheat oven to 425° F. Trim white mushrooms. Remove and discard shiitake stems. Peel and cut sweet potatoes in half lengthwise, then into 1/2 inch slices. Cut onions in 1/2 inch wedges.
Cut garlic cloves in halves. In a large bowl, combine oil, rosemary, salt and pepper. Add mushrooms, sweet potatoes, onions, and garlic; toss to coat. In two shallow roasting pans, arrange vegetables in a single layer. Roast, stirring once, until tender, about 25 minutes. (Mixture can be roasted in advance and reheated in a hot oven.)