Heat 1 teaspoon of oil in a large pan over medium heat.
Add the broccoli and carrots and cook for approximately 4 minutes or until vegetables are tender.
Remove the vegetables from the pan; place them on a plate and cover.
Wipe the pan clean with a paper towel and turn the heat to high.
Add the remaining tablespoon of oil.
Season the chicken pieces with salt and pepper and add them to the pan in a single layer - you may need to do this step in batches. Cook for 3-4 minutes on each side until golden brown and cooked through.
Add the garlic to the pan and cook for 30 seconds.
Add the vegetables back to the pan and cook for 2 more minutes or until the vegetables are warmed through.
In a bowl whisk together the chicken broth, honey and soy sauce.
In a small bowl mix the cornstarch with a tablespoon of cold water.
Pour the soy sauce mixture over the chicken and vegetables; cook for 30 seconds.
Add the cornstarch and bring to a boil; cook for 1 more minute or until sauce has just started to thicken.