Thinly slice the cabbage.
In a small bowl, combine the soy sauce, sesame oil, rice vinegar, and Sriracha sauce. Set aside.
In a large skillet or wok, cook the ground chicken over medium-high heat until no longer pink, breaking it apart into crumbles as it cooks. Remove the cooked chicken from the skillet and set it aside.
In the same skillet, add a little oil if needed, then sauté the minced garlic and ginger until fragrant, about 1 minute.
Add the chopped onion and julienned carrots to the skillet. Cook for 3-4 minutes or until the vegetables begin to soften.
Stir in the thinly sliced cabbage and continue to cook, tossing frequently, until the cabbage is tender yet still slightly crisp, about 5-7 minutes.
Return the cooked chicken to the skillet and pour the prepared sauce over the mixture. Stir well to combine and coat everything evenly. Cook for an additional 2-3 minutes to heat through.
Serve hot, garnished with chopped green onions and sesame seeds if desired.