In a large measuring cup, combine water and cornstarch. Stir until combined and add soy sauce, brown sugar, ginger, garlic, honey, sesame oil, and mirin. Mix well.
Season sliced chicken breast with salt and pepper, then pour ¼ cup (60 ml) of the sauce over the sliced chicken just until covered, and set aside. Mix the sauce with the sliced chicken, cover, and marinate in the refrigerator for at least 30 minutes.
In a large skillet over medium-high heat, pour the rest of the sauce and stir occasionally as it comes to a boil. Once boiling, reduce heat to low and simmer for 10 minutes, or until the sauce has thickened. Set aside in a bowl.
In the same skillet, add 1 tablespoon cooking oil and raise heat back to medium-high. Place sliced chicken pieces in the pan and cook for 3 minutes, flip, and cook an additional 3 minutes. Pour 1 tablespoon of the reduced sauce over the chicken and stir. Remove from the pan and set aside.
Add the remaining cooking oil into the skillet and add the julienned vegetables. Season with salt and white pepper, and cook 3-4 minutes or until vegetables have softened. Add back the chicken and gradually add just enough sauce to coat the chicken and vegetables.
Take ⅓ cup (65 g) of cooked rice and flatten out on a piece of plastic wrap. Layer the cooked chicken and vegetables in the center of the rice and wrap the rice around the fillings. Form into a square shape and repeat with the remainder of the rice and filling. Chill rice balls in the refrigerator for 30 minutes.
Dip the rice ball in beaten eggs, then coat with panko. Shake off any excess bread crumbs.
Heat ½ inch (1 cm) oil in a skillet to 350˚F (180˚C) and fry for 3 minutes on each side or until golden and crispy. Move to a cooling rack, and season with salt.
Cut in half and serve with the remaining sauce for dipping.