Preheat oven to 400˚. Wash and toss beets with olive oil. Place in a roasting pan, cover with foil, and bake until beets are tender, 45-55 minutes (depending on size). Test by inserting a knife- if it's easy, they are done. Remove from oven and let cool.
Once beets have cooled, peel off skin and cut beets into 1/4" cubes. Set aside.
Remove avocado from skin and cut into 1/4" cubes. Place avocado in a bowl and combine with feta cheese. In a small bowl, whisk together olive oil, lemon juice, honey, and salt. Pour over avocado.
Cut the bottom stems off the endives. Carefully peel leaves off and place on a serving tray. On each leaf, place 3-4 cubes of beets, a spoonful of the avocado mixture, and a sprinkling of parsley. Serve immediately.