Preheat oven to 350 degrees. Trim the beet tops, leaving a 1-inch tail, reserving the top greens. Scrub the beets.
Break the garlic up into individual cloves, but don’t peel them. Put the beets and the garlic cloves in a small casserole, add about ½ cup of water and cover with a lid or foil.
Bake until a knife slips easily into the largest beet, about 1 hour; the time will vary depending on the size of the beets.
Meanwhile tear the beet greens off their stems, discarding any yellowed or wilted greens. Cut them into 1-inch ribbons. Set aside.
When the beets are tender, let them cool enough so you can slip off the skins. Trim the tips and tails and cut the beets in wedges or slices.
Squeeze about half the cloves of cooked garlic into a bowl and mash it well with a fork. Add the first 3 tablespoons of olive oil, the balsamic vinegar, orange juice, minced onion, salt and cayenne, and whisk together well. Toss the beets with half of this dressing.
Heat the remaining olive oil in a skillet. Add the beet green ribbons. Cook and stir until the greens are wilted and tender. Toss in the remaining dressing. Season to taste with salt and pepper.
Transfer the greens to a serving plate. Arrange the dressed beets over the greens. If desired, sprinkle with crumbled feta cheese.