Position one oven rack in upper third of oven. Preheat oven to 425 degrees F. Place a 15x10-inch baking pan on upper rack and a large oven-going skillet on lower rack; heat 5 minutes. Meanwhile, in a large bowl combine beets, turnips, carrots, onion, and thyme. Drizzle with oil and sprinkle with 1 tsp. of the salt and the pepper; toss to coat.
Carefully add vegetable mixture to hot baking pan and dry bulgur to hot skillet. Roast 10 minutes, shaking skillet once. Stir broth, ginger, and remaining 1/4 tsp. salt into bulgur; cover with foil. Roast 5 minutes. Remove skillet from oven.
Stir garlic into vegetable mixture. Roast 20 minutes more or until vegetables are tender, stirring once. Remove from oven. Remove and discard thyme sprigs. Stir vinegar into vegetables; stir in bulgur mixture. Drizzle with honey and, if desired, serve with lemon wedges and/or crumbled goat cheese.