Peel and cut the turnips into ¾ inch cubes. Peel (or scrub) the carrots and cut into ½ inch slices. Zest the lemon using a zester or box grater and cut in half, remove seeds as needed.
Heat olive oil in a large skillet over medium high heat. Add turnips and carrots in a single layer (as much as possible) and cook for 4 minutes without turning.
Stir and continue cooking until brown on all sides, 4-5 more minutes.
Add broth, thyme, and lemon zest. Reduce heat to medium low, cover and cook until vegetables are soft, about 8 minutes.
Uncover and increase heat to medium high. Add honey and cook about one minute until the liquid begins to glaze.
Squeeze in the juice of half a lemon and stir it in. Add salt and pepper to taste and serve.