1. In a pan over medium-high heat, melt 1 tablespoon butter. Add 1/3 of the carrots, turnips and potatoes, cut side down, and cook until browned, 3 to 5 minutes; transfer to a plate.
2. Brown the remaining vegetables in 2 batches, melting 1 tablespoon butter before cooking each batch.
3. Return all the vegetables to the pan and add the remaining 1 tablespoon butter, the broth, sugar, salt and pepper. Cover and cook until the vegetables are tender, about 10 minutes.
4. Uncover and cook, stirring occasionally, until the liquid has evaporated and the vegetables are glazed, 3 to 4 minutes more. Transfer the vegetables to a platter and serve immediately. Serves 6-8.