Preheat the oven to 400°. Put the beets in a roasting pan, drizzle the olive oil over them, and season with salt and black pepper to taste. Bake for 35 - 40 minutes, or until they are tender when poked with a fork. Remove them from the oven and let cool for about 10 minutes.
While the beets are roasting, make the vinaigrette.
Peel the zested orange. Section the orange, and arrange the orange and beet slices on a plate. Dribble the vinaigrette all over them, and garnish with the whole basil leaves.
Put the orange zest, balsamic vinegar and chopped basil into a bowl. Whisking constantly, drizzle the olive oil in. Add salt and black pepper to taste.