Combine the first 5 ingredients in a Dutch oven over medium-high heat. Bring to a boil; cover, reduce heat, and simmer for 12 minutes or until the chicken is done. Remove chicken from pan, discarding liquid and solids, and cool chicken slightly. Shred the meat with 2 forks to measure 3 cups.
Combine egg substitute and next 6 ingredients (egg substitute through minced garlic) in a food processor, and process until smooth. Place the chicken and the honey mixture in a medium bowl; toss to coat.
Line plates with salad greens, and top each serving evenly with chicken salad, cucumber, tomato wedges, and oranges.