Cut off the greens of the beets and wash them gently, trying not to break the skin. Place them in a pot and pour water until beets are covered. Cover the pot and bring to a boil. Simmer until beets are tender and easily pierced with a knife.

Allow to slightly cool then carefully remove skin. Slice the beets into rounds, about 1/2-inch thick.

In a small bowl, whisk together balsamic vinegar and olive oil. Dip the beet slices in balsamic-olive oil mixture.

Assemble beets by placing as much as you like of feta cheese between each layer, and re-stacking to form a full beat.

Drizzle stacks with remaining balsamic-olive oil mixture and garnish with basil.