In a small bowl, whisk together the soy sauce, mirin, oyster sauce, brown sugar, and toasted sesame oil. Set aside.

Cook the udon noodles according to package directions. Drain and rinse with cold water to prevent sticking. Set aside.

Heat vegetable oil in a large skillet or wok over medium-high heat. Add the sliced chicken and cook until browned and cooked through. Remove from the skillet. Add the sliced onion and minced garlic, and sauté for 1 minute until fragrant.

Add the sliced mushrooms and julienned carrots to the skillet. Stir-fry for 3-4 minutes until they begin to soften. Add the chopped bok choy and cook for another minute until just wilted.

Return the cooked chicken to the skillet along with the cooked udon noodles. Pour the prepared sauce over everything. Toss gently to combine, cooking for 1-2 minutes until everything is heated through and well-coated. Serve immediately, garnished with sliced green onions and toasted sesame seeds.