In a large Ziploc bag, combine the chicken, soy sauce, ginger, and cornstarch. Shake to coat. Marinate for 30 minutes, turning frequently.
Heat 1 tablespoon of oil over high heat in a large skillet or wok. Add chicken and cook for 3-4 minutes or until it is cooked through, stirring several times. Cook in small batches removing the cooked chicken to a plate.
Heat ½ tablespoon of oil in the skillet over high heat. Add the onions and bell peppers, and cook for 4 minutes or until crisp-tender; stirring frequently. Remove them to a plate. Add the snow peas and cook for 1-1½ minutes or until crisp-tender. Remove them to a plate with the rest of the vegetables.
If necessary, add another ½ tablespoon of oil to the skillet over medium-high heat. Add the broccoli and cook for 3-4 minutes, stirring frequently. Add 1/4 cup of water and place a lid on the skillet for the last minute of cooking. Remove the brocoli to the plate with the other vegetables.
In a small bowl, whisk the chicken broth, soy sauce, sesame oil, brown sugar, rice vinegar, and cornstarch. If desired, add ginger and/or sambel oleck. Add to the skillet over medium-low heat and cook until thickened
Add the chicken and vegetables back to the skillet and stir to coat and warm.