Bring a pot of water to a boil, and cook the beets 25 minutes, or until tender. Cool, peel, and slice 1/3 inch thick. Place slices in a bowl with the tarragon vinegar, and marinate 15 minutes.
Place a few beet slices on a microwave-safe dish, reserving vinegar. Sprinkle beets with some of the reserved vinegar, lemon juice, feta cheese, and walnuts. Top with more beet 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.
