Place fresh whole beets in a large saucepan. Cook, covered, in boiling water for 40 to 50 minutes or until tender; drain. Cool slightly; slip off skins and cut into thin strips.
Meanwhile, for dressing, combine salad oil, white wine vinegar, orange peel, orange juice, green onion, mint, and honey in a screw-top jar. Cover and shake well.
Combine beet strips and half of the dressing in a mixing bowl. Cover and refrigerate the beet mixture and the remaining dressing for 2 to 24 hours.
To serve, combine torn romaine and chopped apple in a mixing bowl. Toss apple mixture with the remaining dressing. Using a slotted spoon, spoon beet mixture over apple mixture in bowl. Makes 8 servings.