Preheat the oven to 450 degrees F. Line a baking sheet with parchment paper.
Scrub the beets well, trim the ends and then slice into 1/4-inch-thick rounds. Lay the beets on the prepared baking sheet in a single layer. Sprinkle 2 tablespoons water over the beets-this will create steam to help cook the beets faster. Season with 1/2 teaspoon salt and a few grinds of pepper. Cut the butter into pea-size cubes and dot the top of each round with 1 or 2 cubes. Cover the pan tightly with foil. Roast until the beets are tender with no resistance when pierced with a fork or skewer, about 20 minutes. Remove the foil and allow the beets to cool, about 5 minutes.
Meanwhile, toast the caraway seeds in a small, dry skillet over medium-high heat until aromatic, about 2 minutes. Transfer to a cutting board to cool. Chop the chives and combine with the yogurt in a small bowl. When the caraway has cooled, finely chop and add to the yogurt. Season with salt and stir well to incorporate.
Put half the beet rounds on a platter. Top each with a teaspoon of yogurt, then another beet round and another teaspoon of yogurt. Serve immediately.
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