In a medium bowl, toss together the chicken, 1 Tbsp. of the hoisin sauce, and 1 Tbsp. of the cornstarch. Set aside.
Whisk together the remaining 2 Tbsp. hoisin sauce, 1 Tbsp. cornstarch, broth, vinegar, brown sugar, chili-garlic sauce in a small bowl; set aside.
Heat a nonstick wok or large, deep skillet over medium-high heat for three or four minutes. Add the oil and then the chicken. Stir-fry until almost cooked through, 2-3 minutes. Add the ginger and garlic, cook for another 15 seconds.
Add in the bell pepper, carrots, and peanuts. Stir fry until tender-crisp, 2 minutes. Pour in the hoisin sauce mixture and cook, stirring constantly, until the mixture boils, and chicken is cooked through (about one minute). Serve hot over a bed of white rice.