1. Bring a large pot of water to a boil. Prepare an ice bath; set aside. Score an X on the bottom of each tomato with a paring knife. Add tomatoes to the pot. Boil until skins are loosened, about 30 seconds; remove tomatoes with a slotted spoon (keeping water at a boil), and immediately plunge them into the ice bath. Drain, peel, and seed tomatoes, then coarsely chop flesh.

2. Add turnips to pot; boil until just tender when pierced with a fork, 3 to 5 minutes. Using a slotted spoon, transfer the turnips to a colander to drain. Repeat process with parsnips, then potatoes. Add broccoli rabe to pot, and boil until bright green and crisp-tender, about 1 minute. Drain in colander; set aside.

3. Heat oil in a large, heavy skillet over medium heat until hot but not smoking. Add onion, garlic, salt, red-pepper flakes, thyme, and reserved turnips, parsnips, and potatoes; spread evenly to cover bottom of skillet. Cook, without stirring, until vegetables begin to brown on bottom, about 15 minutes.

4. Add reserved tomatoes and broccoli rabe to skillet. Stir once; cook until vegetables are very tender and browned, about 25 minutes. Serve hot.