In a medium bowl, combine the mayonnaise, rice vinegar, tomato paste, and 1 tablespoon of low-sodium soy sauce. Mix well until smooth. Add the bite-sized pieces of chicken to the marinade, ensuring each piece is well-coated. Let it marinate for at least 30 minutes, or up to 2 hours in the refrigerator for deeper flavor.
While the chicken marinates, chop the onion, zucchini, carrot, and mushrooms. Set aside in a bowl, ready to be added to the skillet later.
In a large skillet or wok, heat 1 tablespoon of canola oil over medium-high heat. Once hot, add the marinated chicken in a single layer. Cook for about 5-7 minutes, stirring occasionally, until the chicken is golden brown and cooked through. Use a meat thermometer to ensure it reaches an internal temperature of 165°F (75°C).
Remove the cooked chicken from the skillet and set it aside. In the same skillet, add the remaining 1 tablespoon of canola oil and 1 tablespoon of unsalted butter. Once melted, add the onion and sauté for 2 minutes until slightly softened. Then, add the zucchini, carrot, and mushrooms. Stir-fry for an additional 5-6 minutes, or until the vegetables are tender but still crisp.
Return the cooked chicken to the skillet with the vegetables. Pour in the remaining 1 tablespoon of low-sodium soy sauce and toss everything together for a minute or two, allowing the flavors to meld. If you like a bit of heat, sprinkle in some red pepper flakes to taste.
Serve the Hibachi Chicken and Vegetables over a bed of cooked rice or noodles. Garnish with sliced scallions and a sprinkle of toasted sesame seeds for that authentic touch. Enjoy the flavors of your homemade hibachi right at your dining table!
