1. Place beets in a sauce pan of cold water. Bring to a boil, reduce heat and simmer until beets are easily pierced with the tip of a knife. Drain, cool, peel and slice thinly.
2. Peel the oranges and remove the segments over a bowl to reserve the juice.
For the Vinaigrette:
1. Place all of the ingredients for the vinaigrette plus the reserved orange juice in a container with a tight fitting lid. Shake well.
2. Adjust the salt and pepper to taste.
3. Toss the fennel with half of the vinaigrette and arrange fennel slices in a large ring on a serving platter.
4. In the same manner, dress the beet slices with the remaining vinaigrette and arrange them in a ring just inside the fennel.
5. Place the orange segments in the center of the salad.
6. Scatter the onion rings over the entire salad.