Cook the ground chicken until browned and cooked through, then set aside.
Warm the olive oil in a large, deep skillet over medium-high heat and sauté the onion, carrots, and green and red cabbage until they start to soften.
Add in a splash of water to help prevent sticking. The water should immediately sizzle when you add it to the pan, creating steam.
Cover the skillet and lower the heat, cooking until the vegetables are tender, about 10 to 15 minutes depending on how crunchy or soft you want the vegetables to be.
In a glass measuring cup, stir together the tamari, olive oil, sesame oil, garlic, and ginger.
Add the cooked ground chicken to the vegetables and pour the sauce over top. Stir to combine the ingredients.
Serve over a bed of rice and garnish with green onions and sesame seeds.