Preheat your oven to 400°F. Wrap the beets in aluminum foil and roast for about 45-60 minutes, or until tender. Allow to cool, then peel and dice.
In a large bowl, combine the roasted beets, diced cucumber, crumbled feta cheese, and red onion.
In a small bowl, whisk together the olive oil, balsamic vinegar, salt, and pepper.
Pour the dressing over the salad mixture and gently toss to combine.
Sprinkle the fresh dill on top and toss again lightly.
Chill the salad in the refrigerator for at least 30 minutes before serving to allow the flavors to meld.