Place the beet slices in a mixing bowl, and add 1 Tbsp oil and a couple pinches of salt and pepper, and toss to coat evenly.
Take another mixing bowl, and add the potato sweet potato slices, 2 Tbsp oil, and a few pinches of salt and pepper. Toss to coat evenly. Keep the onion slices separate so they remain in tact.
Grease a round baking dish (glass, if possible, to get the full visual effect) with the remaining oil. Begin stacking layers of the root vegetables in a pattern. Once the stack gets too big to continue to hold, place it in the baking dish, then begin adding the layers the same way, by stacking them in your hand, or by adding them to the baking dish itself following the sequence you created.
Do this the entire way around, then create a second circular layer inside, if possible. If not, create a small, linear continuation of the pattern on the inside layer, as shown.
Sprinkle another pinch or two (or three) of salt and pepper over the top, to taste. Place a few sprigs of fresh thyme over the top, and place in the oven. Bake until fork tender, about 30 minutes.
Cool for 10 minutes. Serve warm or at room temperature.