In a medium bowl, combine the chicken pieces, beaten egg, and 1 tablespoon of soy sauce. Toss well to coat the chicken evenly.

Add the cornstarch to the bowl and stir vigorously until a thick, sticky batter forms on the chicken. Let it rest for 5 minutes while you prepare the sauce.

In a separate small bowl, whisk together the remaining 3 tablespoons of soy sauce, hoisin sauce, rice vinegar, brown sugar, and chicken broth until the sugar is fully dissolved.

Heat the vegetable oil in a large skillet or wok over medium-high heat until it reaches 350°F, or until a pinch of cornstarch sizzles immediately upon hitting the oil.

Carefully add the coated chicken to the hot oil in a single layer, cooking in batches if necessary to avoid overcrowding. Fry for 4-5 minutes per side until deeply golden brown and crispy.

Remove the cooked chicken with a slotted spoon and transfer to a paper towel-lined plate to drain. Carefully drain and discard all but 1 tablespoon of the frying oil from the skillet.

Return the skillet to medium heat and add the minced garlic, grated ginger, and dried red chilies. Sauté for about 30 seconds until highly fragrant, being careful not to let the garlic burn.

Pour the prepared sauce mixture into the skillet and let it simmer for 2-3 minutes until it naturally thickens into a glossy, sticky glaze.

Return the crispy fried chicken to the skillet, drizzle with sesame oil, and toss gently to coat every piece evenly in the hot sauce. Serve immediately over warm steamed rice, garnished with sliced green onions.