Preheat the oven to 350 degrees F. Spread the walnuts on a baking sheet and roast until golden, 10 to 12 minutes; let cool slightly, then chop.
Meanwhile, make the dressing: Whisk the yogurt, blue cheese, shallot and 1 tablespoon water in a large bowl; whisk in another tablespoon of water if the dressing is too thick. Season with salt and pepper.
Add the spinach, tomatoes, hearts of palm, cucumbers and beets to the bowl with the dressing and toss. Add the chicken and toss again. Divide among plates and top with the walnuts. Season with salt and pepper. Serve with the rolls.