In a 12-inch nonstick skillet, heat the oil over medium heat. Add the carrots, parsnips, shallots, thyme sprigs, bacon, and 1 tsp. salt; toss well to coat.
Cover the pan with the lid ajar by about 1 inch. Cook, stirring occasionally, until the shallots are limp and lightly browned and most of the carrots and parsnips have a little bit of brown on them, 8 to 12 minutes. As the mixture cooks, you should hear a gentle sizzle.
Uncover, turn the heat down to low, and cook, stirring occasionally and then gently pushing the vegetables back into a single layer so that most have direct contact with the pan, until the vegetables are tender and nicely browned, 12 to 16 minutes.
Remove the pan from the heat and discard the thyme sprigs. Stir in the orange-honey mixture and the thyme leaves, and season to taste with salt. Serve right away or let sit off the heat, partially covered, until ready to serve, and then reheat gently over medium-low heat.