Preheat the oven to 400 degrees F. Grease a 12-inch cast iron skillet.
Prepare the beets and turnips by trimming and scrubbing them (you can also peel them if you'd like). Use a mandoline to make thin slices. Layer the vegetables in the cast iron skillet (or other oven-proof skillet or 9x13 baking dish) by starting with a layer of turnips, followed by a layer of beets, and so on.
In another large skillet, heat 2 tablespoon olive oil over medium heat. Add the diced shallots and cook for 3 to 4 minutes. Remove from heat and stir in the other 4 tablespoon of olive oil and 2 tablespoon of butter until melted. Add the chopped thyme and vegetable stock. This is your gratin sauce.
Pour the sauce over your layered vegetables. Wrap foil over the skillet and bake for 45 minutes. Remove from oven, take off the foil, and sprinkle the shredded gruyere cheese over the vegetables. Bake uncovered for another 15 minutes or until the cheese is bubbling and slightly brown.
Garnish with fresh thyme sprigs. Serve warm and enjoy!
Notes
You can use larger beets for this recipe if you can't find baby ones.
When layering the gratin, try to make each consecutive layer further away from the edge of the skillet than the one before it. This will make for a really pretty dish, but you can also just make flat layers, as you would with a scalloped potato dish.
If you are making this in advance, you can reheat the entire gratin in its skillet, covered with foil, for 10 to 15 minutes at 350 to 400 degrees F. But it does taste best fresh out of the oven.
If you don't have a mandoline, you can try using a sharp knife, but it will take longer.