Begin by preparing the chicken. Dice the chicken breasts into 1-inch cubes and season with salt and black pepper. Set aside.
For the hibachi sauce, combine the yellow onion, garlic, ginger, soy sauce, rice wine vinegar, chinkiang vinegar, lemon juice, brown sugar, and pepper in a blender. Pulse until the mixture reaches a smooth consistency.
Heat vegetable oil in a large skillet over medium-high heat. Add the seasoned chicken pieces and sear them on all sides until they reach a light golden color.
Once the chicken is seared, add the sliced carrots and chopped zucchini to the skillet. Pour in about half a cup of the hibachi sauce, and sauté the mixture until the chicken is cooked through, and the sauce has thickened. Add additional sauce as needed, stirring occasionally.
Remove the chicken and vegetables from the skillet and serve them over warm rice. Garnish with chopped green onions and drizzle with yum yum sauce to complete the dish.