Add mushrooms, zucchini, and onions to a microwave-safe bowl. Cook in microwave for 4-5 minutes to soften. Set aside.
Place the beaten egg in one shallow bowl and cornstarch in another bowl. Toss the chicken in beaten egg and then lightly coat each piece with cornstarch.
Coat a large nonstick pan with cooking spray. Heat canola and sesame oil in pan. Add chicken and cook on medium-high until browned on both sides, about 2-3 minutes on each side. Remove chicken from the pan and leave drippings in pan. Set chicken aside.
To the same pan, add garlic and ginger and stir often for 30 seconds. Add the softened mushrooms/zucchini/onions and continue to cook for 4-5 minutes until zucchini is cooked through.
In a small bowl mix together the soy sauce, rice wine vinegar, and honey. Add chicken back pan and stir to coat. Pour in soy sauce mixture and mix everything together. Continue to cook for a few minutes while stirring.
Serve over cauliflower rice or brown rice, if desired. See serving tips below.