In a medium bowl, combine the toasted sesame oil with the egg white, 1 tablespoon of the soy sauce and 1/4 cup plus 2 tablespoons of the cornstarch. Add the chicken, stirring to coat. Let stand at room temperature for 20 minutes.
Meanwhile, in a small bowl, whisk the chicken broth with the chile-garlic sauce, sugar and the remaining 1/4 cup of soy sauce and 1 tablespoon of cornstarch.
In a large saucepan, heat the 1 tablespoon of oil. Add the ginger and garlic and cook over high heat until fragrant, about 1 minute. Stir the broth mixture, add it to the pan and cook until thickened and glossy, about 3 minutes. Keep the sauce warm over low heat.
In a large, deep skillet, heat 1/2 inch of oil until shimmering. Carefully add the chicken, one piece at a time, and fry over high heat, turning once or twice, until very browned and crisp, about 4 minutes. Drain the chicken on paper towels and immediately add to the sauce along with the scallions. Cook just until coated, about 30 seconds. Serve right away, with steamed broccoli and rice.