Trim the beets, leaving the root and about 1 inch of the stem, then scrubbing them with a vegetable brush. Wearing gloves (if you like), peel the beets (the gloves prevent them from staining your hands), and cut them into 1/2-inch thick wedges.
Pan spray a cooking sheet, then drizzle with the oil, tossing once to coat. Bake in oven at 400 degrees F for 45 minutes, stirring twice, or until the beets are tender.
While beets are roasting, prepare the other vegetables and dressing.
Rinse the fennel bulbs to make sure they're thoroughly clean. Remove the tough outer leaves, retaining the feathery fronds. Remove fronds from leaves/stalks and mince them to measure 2 tablespoons. Remove stalks from fennel and discard.
Cut the cleaned bulbs in half, lengthwise, discarding the cores. Cut the divided bulbs into 1/8 to 1/4-inch slices.
Slice the Belgian endives into whatever width you prefer, although it's nice if they're thinner than the fennel pieces.
In a large bowl, combine the fennel, endive, walnuts, spinach, salt, and pepper. Toss gently; set aside.
In a bowl, whisk together the vinegars, honey, orange rind, orange juice, basil, shallot (if using) olive oil, Dijon, nutmeg, and salt.
When beets are done roasting, remove from oven and let cool slightly.
Drizzle the fennel mixture with the whisked dressing, then add the roasted beets. Toss to combine. Tidy up the edges of the serving bowl with a napkin. Garnish the salad with the minced fennel fronds and feta cheese (if using), and serve.