Preheat the oven to 350˚F.
Wash and dry each beet. Wrap each beet individually into a small piece of foil, drizzling a little olive oil on top of the beet before sealing the foil. Transfer the foil packets to a sheet pan and roast in the oven for approximately 45 minutes – 1 hour, or until a knife can be easily inserted into the centre of the beet. Remove from the oven and set aside to cool.
Once the beets are cool enough to handle, unwrap and slice each beet into four equal slices. From one beet, I typically am able to make two stacks. Each stack will have a beetroot slice as the base, then a slice of feta, another slice of beetroot and a final top slice of feta. Sprinkle with some fresh thyme leaves, another little drizzle of olive oil, and a twist of salt and pepper. Wrap each stack in its own foil packet (re-use the ones from earlier if you can). Place each foil packet back on the sheet pan and roast for an additional 15 minutes.
Open the foil packets and return to the oven for the final five minutes so the cheese starts to color. Serve immediately while warm.
If you are short on time, you can use pre-cooked beets. I have also tried this recipe using whole pickled beets and it worked fine.