Preheat oven to 325°F/160°C. Lightly coat a 9x13 and 8x8 pan with cooking spray.
Cut the boneless chicken breasts into 1-inch chunks. Season with salt and pepper. Place the chicken in a gallon-sized resealable bag with the cornstarch, seal bag, and toss to coat the chicken.
Whisk the eggs in a shallow dish (a glass pie plate works well), then take a large handful and dip each chicken piece in the egg. Meanwhile, heat 1/4 cup oil in a large skillet over medium heat until hot and rippling. Fry coated chicken pieces in the hot oil. You will need to do one single-layer amount of chicken at a time, so it ends up being about 5 batches. Cook for about 30 seconds on each side until golden, but not cooked through. Place the chicken pieces on a paper towel-lined plate; then transfer chicken to a prepared baking dish in a shallow layer. You may need to add and heat another 1/4 cup of oil about halfway through.
Whisk sauce ingredients together and pour over chicken. Bake for about 1 hour, turning chicken three times while cooking so it is evenly coated with the sauce. Serve over rice.