Bring a pot of salted water to a boil and add the beets. Simmer about 35 minutes until the beets are tender and a fork goes through easily. Strain and toss with the oil, vinegar, and mustard in a large bowl. Allow to cool in the fridge for at least one hour
Meanwhile, Mix the garlic, lemon, dill, and salt and pepper into the yogurt. Set aside in the fridge until ready to use.
Stir the cucumber into the beets. Season with a pinch of salt and pepper. Pour out onto a serving platter. Spoon the yogurt mixture onto the top of the beets, putting several dollops of yogurt in various spots spread out over the top of the salad. top with some dill sprigs and serve.