Pour vegetable oil into a large skillet to a depth of about 2 inches and heat over medium-high until hot (careful not to smoke).
In a large bowl combine the chicken pieces, all-purpose flour, cornstarch, and baking soda; add the ice-cold water and stir until the chicken is evenly coated with a smooth batter resembling thick pudding.
Carefully add chicken pieces to the hot oil in batches so they do not crowd the pan.
Fry the chicken about 8–10 minutes total, turning once halfway through, until golden brown and an instant-read thermometer inserted into the center reads 165°F (74°C).
Remove fried chicken to a plate lined with paper towels to drain and keep warm.
In a separate small skillet over medium heat, combine the butter, white sugar, soy sauce, and honey; stir frequently until the mixture comes to a gentle bubble, then cook for 1 minute more.
Remove the glaze from the heat and pour it over the drained fried chicken; toss or stir gently to coat each piece evenly.
Serve immediately, garnished with chopped fresh parsley if using.