Combine chicken, 1T hoisin, 1T cornstarch in bowl; toss well to coat and set aside.
Combine remaining 2T hoisin, 1T cornstarch, broth, vinegar, sugar, and chili garlic sauce in bowl; set aside.
Heat wok (or large pan) over med-high heat until a drop of water sizzles on it. Pour in oil, swirl to coat; then add chicken. Stir fry for 3 minutes. Add ginger and garlic; stir fry another 15 seconds. Add bell pepper, carrots, and peanuts; stir fry 2 minutes. Add hoisin sauce mixture stirring constantly until mixture boils and thickens.