In a bowl, whisk together the chicken broth, soy sauce, rice vinegar, honey, brown sugar, minced garlic, chili garlic sauce, grated ginger, onion powder, and toasted sesame oil until the sugar dissolves completely. Reserve 1/3 cup of this marinade in a separate container for later use as your sauce base. Place the chicken pieces in a zip-top bag or shallow dish and pour the remaining marinade over them, ensuring all pieces are well coated. Seal and refrigerate for at least 2 hours, though up to 12 hours will develop deeper flavor. I find that marinating overnight gives the chicken a more complex taste, so plan ahead if you can.
While the chicken marinates (or just before cooking), cut the large onion into 1/2-inch thick wedges and slice the bell pepper into bite-sized strips. In a small bowl, whisk the cornstarch with 2 tablespoons of water to create a slurry that will thicken your sauce—this prevents lumps from forming. Have all your vegetables measured and ready to go in one place, as stir-frying happens quickly once you start cooking.
Heat the sesame oil and unsalted butter in a large skillet or wok over medium-high heat until the butter is foaming and the pan is very hot. Working in batches if necessary to avoid crowding, carefully lay the marinated chicken pieces in a single layer. Let them cook undisturbed for 5-7 minutes until they develop a golden-brown crust and are cooked through. I like to resist the urge to move the chicken around—letting it sit creates that beautiful caramelization that adds depth to the dish.
Add the prepared onion wedges, bell pepper slices, and mixed stir-fry vegetables to the pan with the cooked chicken. Increase the heat to medium-high and stir-fry everything together for 3-4 minutes, allowing the vegetables to develop slight color while remaining crisp-tender. The high heat at this stage will caramelize the vegetable edges and blend the flavors with the cooked chicken.
Reduce the heat to medium and pour the reserved marinade from Step 1 into the pan along with the cornstarch slurry from Step 2, stirring constantly. Simmer for 1-2 minutes until the sauce thickens and becomes glossy, coating all the chicken and vegetables evenly. The cornstarch will help the sauce cling to the ingredients, creating that signature stir-fry texture. Remove from heat immediately once the desired thickness is reached to prevent overcooking the vegetables.