To make the filling, combine 3 tablespoons of the soy sauce, 1 clove of minced garlic, half of the green onions, and 1 tablespoon of the oil in a resealable bag; shake well to combine. Place the chicken in the bag, press out the excess air, and seal. Refrigerate and allow to marinate at least 30 minutes or up to 3 hours. Heat 2 tablespoons of the oil in a wok or large skillet over high heat. When the oil is very hot, add the chicken pieces to the pan and cook, stirring constantly, until the chicken is cooked through and lightly browned. Remove to a plate and set aside. Add the remaining tablespoon of oil to the pan. Add the shredded cabbage and carrots, and the remaining tablespoon of soy sauce. Stir to toss the vegetables. Cook over high heat for about 2 minutes. Toss in the bean sprouts, remaining garlic and green onions and cook for 1 minute more. Remove from the heat. Dice the chicken breasts and add them to the vegetable mixture. Place the mixture in a colander or mesh strainer in the sink or a large bowl. Press down firmly on the filling mixture to remove as much excess liquid as possible. Let the filling cool for 30 minutes before filling the wrappers. To finish the egg rolls, heat about 3 inches of oil in a Dutch oven to 375? F. While the oil is heating, assemble the rolls. Lay an egg roll wrapper out on a work surface with one corner pointing toward you. Add a tablespoon or two of the filling to the center of the wrapper. Fold the corner closest to you up over the filling. Roll slightly away from you, fold the two corners pointing to the sides inward, and continue rolling the wrapper tightly away from you. Dip a finger in the cornstarch mixture and lightly brush inside the top corner of the wrapper to help adhere, and finish rolling. Repeat with the remaining wrappers and filling.