In a small saucepan, combine soy sauce, water, mirin, brown sugar, honey, minced garlic, grated ginger, and cornstarch slurry. Whisk the mixture thoroughly and bring it to a gentle simmer over medium heat. Stir continuously for about 5 minutes, or until the sauce thickens to a glossy consistency, then set aside.

Season your boneless skinless chicken thighs with salt and pepper, ensuring they are evenly coated. Pour 1/4 cup of the prepared teriyaki sauce over the chicken, tossing to coat each piece well. Allow the chicken to marinate for at least 15 minutes.

Heat a large wok or skillet over medium-high heat and add a splash of vegetable oil. Once the oil is hot, add the marinated chicken thighs to the pan. Stir-fry for about 5 minutes, or until the chicken is browned and cooked through, reaching an internal temperature of 165°F. Remove the chicken from the pan and set aside.

In the same wok, add another drizzle of vegetable oil if needed. Add sliced onions and julienned carrots, stirring constantly for about 3 minutes until they begin to soften. Then mix in broccoli florets and sliced cabbage along with minced garlic and grated ginger. Continue to stir-fry for an additional 2-3 minutes.

Meanwhile, bring a pot of water to a boil and cook the udon noodles according to the package instructions, usually around 3-5 minutes. Once cooked, drain the noodles in a colander and rinse them briefly under cold water.

Return the cooked chicken to the wok with the sautéed vegetables. Add the cooked udon noodles and the remaining teriyaki sauce to the pan. Toss everything together gently for about 1-2 minutes until heated through.

Plate your Chicken Teriyaki Noodles, and finish with a sprinkle of sliced green onions and sesame seeds. Serve hot.