Place the sesame seeds in a dry skillet over medium heat. Cook, stirring frequently, just until lightly browned and fragrant. Set aside to cool.
Toss the chicken pieces with egg, 3 tablespoons cornstarch, and soy sauce. Refrigerate for 15 minutes.
Meanwhile, in a small bowl, whisk together broth, brown sugar, 2 tablespoons cornstarch, soy sauce, sesame oil, ginger, and garlic.
In a 10-inch skillet, heat the vegetable oil over medium-high heat. Add half of the chicken and stir-fry until browned and almost cooked through, about 5 minutes. Transfer the fried chicken to a bowl and repeat with the remaining chicken.
Whisk the sauce and add it to the skillet along with all of the chicken and cook over medium-high heat while stirring until thickened, about 3 to 4 minutes. Stir in the sesame seeds.
Garnish with green onions.
