Leave root and 1 inch of stem on beets; scrub with a brush. Place beets and fennel seeds in a medium saucepan; cover with water, and bring to a boil. Cover, reduce heat, and simmer 35 minutes or until tender. Drain beets through a fine sieve into a bowl, reserving fennel seeds and 3 cups cooking liquid. Rinse beets under cold water; drain. Peel beets; cut into 1/2-inch cubes, reserving 3/4 cup for garnish. Combine remaining beets, reserved cooking liquid, and fennel seeds in a bowl; set aside.
Combine 1/4 cup water and oil in a medium nonstick skillet; place over medium-high heat until hot. Add fennel bulb and onion; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until tender.
Combine fennel bulb mixture, beet mixture, buttermilk, salt, and pepper in a food processor or blender; process until smooth. Pour soup into a bowl; cover and chill thoroughly. Ladle 3/4 cup soup into individual bowls, and top with 2 tablespoons reserved beets.