In pan, cover chicken with 1 inch of water; simmer, 10 minutes. Remove from heat; let chicken sit for 10 minutes. Cut into chunks; chop in food processor. Mix chicken, apple and 1/4 cup mayo in bowl; season. Trim crusts from bread; flatten with rolling pin, then spread with more mayo; spoon 2 tbsp. chicken salad near 1 edge of each slice; top with a few veggie strips. Roll up like sushi. Chill, 10 minutes; cut into slices.