Preheat oven to 375°.
Leave root and 1 inch of stem on beets; scrub with a brush. Place beets on a large sheet of aluminum foil; sprinkle beets with water. Wrap beets in foil; arrange packet of beets and onion on a baking sheet. Bake at 375° for 1 hour or until tender. Cool.
Combine broth, chopped fennel, and apple in a medium saucepan. Bring to a boil; reduce heat, and simmer 15 minutes or until fennel is tender. Cool.
Trim off beet roots; rub off skins, and coarsely chop. Peel and quarter onion. Add beets and onion to broth mixture in pan, stirring to combine. Place half of beet mixture in a blender; process until smooth. Pour pureed beet mixture into a large bowl. Repeat procedure with remaining beet mixture. Stir in vinegar, juice, salt, and pepper. Return pureed beet mixture to pan.
Place the pureed beet mixture over medium heat, and cook 2 minutes or until thoroughly heated. Ladle soup into bowls, and top with sour cream. Sprinkle evenly with chopped fennel fronds.