Preheat oven to 400 degrees F.
Trim greens from beet roots and set aside. Wash beet roots, but do not peel. Wrap each beet root in aluminum foil and place on a baking sheet. Bake until tender, roughly 45 minutes, depending on thickness of beets.
While beets are cooking, wash the greens extra well (beets tend to be sandy) and dry. Slice the beet greens into thin ribbons and put in a large bowl.
When beets are tender, remove from oven, unwrap the foil and let cool 5-10 minutes.
Peel the cooled beets and cut into 1-inch thick pieces. Add to the bowl with the greens.
Add peeled, cut oranges (and any juices) and onion slices to the bowl.
In a separate bowl/jar, mix vegetable oil, vinegar, salt and pepper. Pour over the salad and toss to combine.
If the beet greens are insufficient to serve 6, then add extra clean salad greens (arugula, spring mix or other) to the bowl. Top with crumbled feta cheese, if desired. Serve chilled.