In a small bowl, whisk the chicken broth, soy sauce, honey, cornstarch, and garlic until they are well combined. Set aside. In a large skillet, heat the oil over medium-high heat. Add the chicken and season with salt and pepper. Cook, stirring occasionally, until the chicken is golden on all side, 6 to 8 minutes. Add the carrots and onion and cook, stirring, for 2 to 3 minutes. Add the broccoli and sauce and to the skillet and mix well. Cover and cook until the broccoli is tender and the sauce has thickened, 3 to 4 minutes. Serve immediately or store in the refrigerator for up to 3 days.