Prep the chicken: Pat the chicken dry with paper towels. Season with salt and pepper.
Toss with the beaten egg to coat.
Coat for crispiness: In a bowl, mix cornstarch and flour. Add the chicken pieces and toss until evenly coated. Shake off excess.
Heat the oil: Pour 1/2 inch of oil into a large skillet or wok.
Heat over medium-high until shimmering. A small pinch of cornstarch should sizzle on contact.
Fry in batches: Add chicken in a single layer, without crowding. Fry 3–4 minutes per side until golden and cooked through.
Transfer to a wire rack or paper towels. Repeat with remaining chicken.
Make the sauce base: In a bowl, whisk soy sauce, honey, rice vinegar, sesame oil, ketchup, garlic, ginger, and 1/2 cup of the water or broth.
Thicken the sauce: Pour the sauce mixture into a clean skillet over medium heat. In a small cup, stir the remaining 1/4 cup water with 1 tablespoon cornstarch to make a slurry.
Drizzle the slurry into the sauce, whisking until glossy and slightly thick, about 2 minutes.
Coat the chicken: Add fried chicken to the pan and toss until every piece is well coated. Cook 1–2 minutes to marry the flavors.
Finish and serve: Sprinkle with sesame seeds and green onions. Serve hot over rice.
For extra shine, add a tiny splash of sesame oil at the end.