Scrub and trim beets, and chop them into bite sized pieces.
Place chopped beets in a large, covered pan along with 2 Tbsp. olive oil and 2 Tbsp. water. Lightly season with salt and pepper and toss well to make sure the beets are coated with oil and seasoning. Cook over medium heat for 20 - 30 minutes, stirring often to avoid burning, until beets are fork tender.
When beets are cooked, remove from the pan and allow to come to room temperature. Place them in the refrigerator to cool down more quickly if needed.
For the vinaigrette: Measure the Dijon, white wine vinegar (and/or Mandarin liquid), honey and olive oil in a small bowl, and whisk to combine.
Add the sliced shallots to the vinaigrette, and stir well. Allow the shallots to "marinate" in the vinaigrette for 15 minutes or so, and stir again. Toss the vinaigrette with arugula/greens. (See Cook’s Notes below about using the vinaigrette for “quick pickled” beets.)
To serve: Plate dressed greens. Using a spoon, sprinkle red beets on top of the greens. If using other, lighter colored beets, sprinkle those on top of the red beets to avoid staining. Finish with segments of Mandarin orange and “crumbles” of goat cheese – as much as you like – and enjoy!