In a large skillet, heat 2 tablespoons of oil over medium-high heat. Add the chicken and garlic. Stir fry for 3 minutes or until the chicken turns white. Add the remaining oil, pepper, snow peas, cashews, and green onion. Stir fry 1 minute.
In a small bowl, whisk together the chicken broth, soy sauce, cornstarch and ginger until smooth. Stir into the chicken mixture. Bring to a boil over medium heat while stirring. Boil 1 minute, or until the mixture thickens a bit.