1. Preheat oven to 400°F (200°C). Wash beets and trim stems. Drizzle beets with oil and wrap them in tin foil. Roast directly on the middle rack of oven until tender, about 1 hour. After 30 minutes prepare feta. While beets are roasting, place feta in a medium sized baking dish. Drizzle with oil and season with black pepper on both sides. Place the baking dish uncovered, on the middle rack of the oven next to beets and bake for 20 to 30 minutes.
2. Remove feta from the oven and let cool at room temperature (not in the 1. fridge) while the salad is being prepared. Once cooled, use a fork to crumble feta by shaving off chunks a little at a time. Test beets for doneness by piercing the largest beet with a fork (it should slide in and out with ease). When beets are done, remove from oven and set in the refrigerator to chill. Once chilled, with a paring knife, peel skin, then cut the beets into ½-inch sized cubes. Set aside.
3. For the salad dressing, combine all ingredients in a jar, cover with a lid, and shake vigorously to blend.
4. In a large bowl, combine mixed greens and cucumbers. Drizzle the salad dressing over it and toss to combine. Serve salad by topping with roasted beets and feta, green onions, and walnuts.