Combine the sauce ingredients in a medium-sized bowl. Stir to mix well and set aside.
Add the chicken, Shaoxing wine, soy sauce, sugar, white pepper, onion, carrot, and garlic into a large bowl. Beat everything together with a spatula until it becomes sticky, about 5 minutes. Add the egg and breadcrumbs and stir to incorporate.
Coat your hands with a light layer of oil (it helps you to form the meatballs without sticking too much to your hands). Add one heaping tablespoon of the mixture into your palm and shape it into a round ball. Place it onto a large flat plate or tray. Repeat to shape the rest of the meatballs.
Heat the vegetable oil in a large skillet over medium heat until hot. Add the meatballs into the pan without overcrowding them. Let the meatballs brown for 1 to 2 minute, then flip and brown the other side for another 1 to 2 minutes. Once both sides are browned, flip the meatballs on their sides and brown for another 4 to 5 minutes. Roll them occasionally to brown all sides evenly. Once done, remove the meatballs onto a large plate and set aside.
Turn the heat up to medium-high. Add the onion and pepper. Stir fry until the onion turns slightly pale golden on the edges, 1 to 2 minutes.
Stir the sauce again to thoroughly dissolve the cornstarch and pour it into the pan. Stirring constantly to bring the sauce to a boil and cook until it is thickened. Turn off the heat and transfer everything to a large serving plate.
Serve the meatballs with the sauce over steamed rice and enjoy as a main dish.