In a large mixing bowl, combine the turkey, cucumber, celery, cranberries, onion, and parsley. Stir the mayonnaise and mustard together and fold into the turkey mixture to coat evenly. Salt and pepper, to taste.
Turn broiler on high and lightly butter cut side of buns. Place buns on a rimmed baking sheet and toast under the broiler for 3 minutes, or until light golden brown.
Serve turkey salad on toasted sprouted wheat buns or over a bed of lettuce. Top with 2-3 slices of avocado for each serving.