Preheat your oven to 400°F (200°C). Wrap each beet in aluminum foil and place them on a baking sheet. Roast for about 45 minutes until tender. Let cool before peeling.
While the beets are roasting, slice your English cucumber into thin rounds.
In a large bowl, gently combine the sliced cucumbers with diced roasted beets.
Crumble feta cheese over the beet-cucumber mixture and sprinkle with fresh dill.
In a small bowl, whisk together olive oil, aged balsamic vinegar, salt, and pepper. Drizzle over the salad before serving.
Toss everything gently until well coated. Serve chilled or at room temperature.