Dry roast the beets. Stand up the trimmed beets - long tail down - in a glass bread loaf pan or a small casserole dish filled with about an inch of kosher salt. Place in a 400 degree oven and roast until tender, 30 to 40 minutes. Allow to cool and slip off the skins. Thinly slice the beets and cut each into quarters.
Make the dressing. Whisk the vinegar, oil, ground pepper and salt together in a small bowl.
Very gently toss the beets, plums, basil, spinach and dressing in a salad bowl. Sprinkle with feta and serve. Divide onto four plates, sprinkle with feta and serve.