Prepare the Dressing: In a small bowl, whisk together the mayonnaise (or substitute), lemon juice, Dijon mustard, minced shallot, chopped tarragon, honey, and salt. Set aside.
Prep the Brussels Sprouts: Trim the ends of the Brussels sprouts and thinly slice them. You can use a sharp knife or a mandoline for even slices.
Combine Ingredients: In a large mixing bowl, combine the sliced Brussels sprouts, apple slices, chopped celery, toasted walnuts, and halved grapes. Toss gently to mix.
Add the Dressing: Pour the prepared dressing over the salad and toss until all ingredients are evenly coated with the dressing.
Garnish and Serve: If using, sprinkle pomegranate seeds over the top for an extra burst of color and antioxidants. Serve the Brussels Sprouts Waldorf Salad immediately, or refrigerate for a few hours to let the flavors meld.