Place a rack in the center of the oven and preheat the oven to 400°F. Place the beets in a 9x13-inch baking dish or similar dish large enough to hold them comfortably in a single layer. Pour a thin layer of water into the bottom of the dish, cover with foil, and bake until the beets feel tender in the center when pierced with a small, sharp knife, 50 minutes to 1 hour 10 minutes or longer depending upon the size of your beets. Transfer the beets to a cutting board and let stand until cool enough to handle. If you are concerned about staining your cutting board, lay a sheet of parchment paper over it first.
While the beets cook, prepare the balsamic dressing: in a medium mixing bowl or large measuring cup, whisk together the dressing ingredients—olive oil, balsamic, mustard, honey, garlic, salt, and pepper.
Once the beets are cool enough to handle but are still warm, with a paper towel, rub away the beet skins. If they are stubborn and stick, peel them with a small, sharp knife. Dice each beet into 3/4-inch pieces (or cut into wedges if you prefer), then place in a large serving bowl. Pour half of the dressing over the warm beets, then stir to coat (the beets absorb dressing better when they are warm).
Add the arugula to the bowl with the beets. Toss to combine. Top with about two-thirds each of the apple, pistachios, cranberries, and goat cheese. Toss once more, adding more of the remaining dressing as desired. The arugula should be lightly moist but not drowning.
Sprinkle the remaining pistachios, cranberries, and goat cheese over the top. Enjoy warm or at room temperature.
Notes
TO MAKE AHEAD: Bake, peel, and dice the beets up to 1 day in advance. Refrigerate them in an airtight storage container. Up to 2 days in advance, whisk the dressing ingredients together. Refrigerate the dressing in an airtight storage container. Assemble the salad as directed when you're ready to serve.
TO STORE: Refrigerate leftover salad in an airtight storage container for up to 3 days.