Combine all the sauce ingredients in a medium bowl and stir until fully combined and cornstarch is dissolved. Set aside.
In a large wok or skillet over medium-high, heat 2 tablespoons of canola oil. Add the chicken in one layer (if needed cook in batches), and cook until golden and done, for about 6-8 minutes, stirring occasionally. Remove chicken from pan and set aside on a plate.
To the same skillet add the remaining tablespoon of oil, add the carrots, stir fry veggies and snow peas. Sauce for about 6-8 minutes, just until tender.
Add back the chicken, give the sauce a good stir and pour it over the chicken. Toss to combine and let the mixture come to a boil, reduce heat to low and simmer for 2-3 minutes, stirring occasionally, until the sauce thickens.
Garnish with sesame seeds and green onion before serving over rice if desired.