Bring a pot of water to the boil and cook the beetroots 25 minutes or until tender. Cool, peel and slice 7.5mm thick. Place slices in a bowl with the tarragon vinegar and marinate 15 minutes.
Place a few beetroot slices on a microwave-safe dish, reserving vinegar. Sprinkle beetroots with some of the reserved vinegar, lemon juice, feta cheese and walnuts. Top with more beetroot slices and sprinkle again with vinegar, lemon juice, feta and walnuts. Repeat, building the stacks as high as you like.
Place stacks in the microwave and cook 40 to 60 seconds on Medium. Cool slightly before serving.