Combine all sauce ingredients together and stir. If you want, you can add a splash of water to loosen it to make it easier to pour into the wok.
In a small bowl, add the cornstarch and just enough water to dissolve it. Stir until there are no more lumps. Set aside.
In a wok, add just enough oil to coat the bottom and heat over medium high heat. Add onion, garlic, and ginger, and stir until the onion is translucent. Add five-spice powder and stir for 30 seconds to toast the spices.
Add ground chicken and break it apart with the spatula. Once there are no more lumps, but the chicken is still mostly raw, add the sauce mixture and keep cooking and stirring until the chicken is almost done.
Add carrots and water chestnuts and stir. Once the chicken is done, crank the heat up to high and cook, stirring constantly, until there is no more sauce pooling at the bottom of the pan.
Add black soy sauce to adjust colour if you wish. Stir the cornstarch slurry again (it will settle over time) and pour into the chicken and stir quickly. This will thicken the sauce and allows the sauce to cling to the chicken pieces rather than run down and pool at the bottom. Turn off the heat.
Toss in green onions. Taste and adjust seasoning, adding more salt if needed.
To serve, put a bit of diluted hoisin paste or hoisin sauce on a piece of iceberg lettuce. Put the chicken filling on top, drizzle with toasted white sesame seeds and enjoy!