In a large pan, heat 1 teaspoon of vegetable oil over medium heat. Add the broccoli and carrots, cooking for about 4 minutes or until the vegetables are tender. Once done, remove the vegetables and set them aside on a plate, covering them to keep warm.
Wipe the pan clean with a paper towel and increase the heat to high. Add the remaining tablespoon of oil to the pan.
Season the chicken pieces with salt and pepper. Add them to the pan in a single layer (you may need to do this in batches). Cook for 3-4 minutes on each side, or until the chicken is golden brown and fully cooked.
Add the minced garlic to the pan and sauté for 30 seconds.
In a small bowl, whisk together the chicken broth, honey, and soy sauce.
In another bowl, mix the cornstarch with 1 tablespoon of cold water to create a slurry.
Pour the soy sauce mixture over the chicken and vegetables. Cook for 30 seconds, then stir in the cornstarch mixture and bring to a boil. Let it cook for another minute or until the sauce starts to thicken.
Serve immediately, preferably with rice.