Trim the green tops from the beets, leaving only about a 1/4-inch of the stalk. Wash but do not peel, and place the whole beets in enough boiling water to cover. Cook them over medium-low heat until they are just tender (45 minutes to an hour and a half, depending on the age and size of them). When they reach the just tender stage, drain them and rinse them briefly in cold water. Trim off the roots and tops and slip off their skins, Cut them into 1/2-inch dice and set aside.
In a large, heavy saucepan, heat the butter or margarine until it foams. Sprinkle in the cornstarch until it is well-blended. Stir in the vinegar, then slowly add the orange juice, stirring quickly to avoid lumps. Add the honey, salt, and pepper. Add the diced beets and stir everything together thoroughly. Cook over low heat for 20 minutes.