Cut 2 pounds boneless skinless chicken breasts into bite-sized pieces and place in a large bowl. Crack 1 large egg on top of the chicken and massage it in with your hand to coat the chicken.
Transfer the chicken to a ziplock bag. Add 1 cup cornstarch, seal the bag, and toss to coat each chicken piece well. Add cornstarch if needed.
In a large skillet or wok over medium-high heat, add ⅓ cup vegetable oil. Working in batches, add the coated chicken and cook for 7-8 minutes until browned and no longer pink. Remove the chicken from the pan and set it aside.
In a medium bowl, whisk together ¾ cup hoisin sauce, ¼ cup soy sauce, ¾ cup brown sugar, 2 cloves minced garlic, ¼ cup rice vinegar, 2 teaspoons sesame oil, ½ teaspoon ground ginger, and 1 teaspoon crushed red pepper.
Returning to the skillet or wok, add the sauce and bring it to a simmer while stirring. Let it simmer for 2-3 minutes to help slightly thicken the sauce. Add the chicken and toss to coat.
Add the chicken and toss to coat. Cook for 2-3 minutes and enjoy over rice! Garnish with sliced green onions and additional red pepper flakes, if desired.