In a bowl, mix the honey, soy sauce, chicken broth, garlic and black pepper, and pour into the Instant Pot.
Add chicken in one layer (try not to overlap).
Set the instant pot to Pressure Cook for 8 minutes.
Once it has finished pressure cooking, do a quick release of the steam valve. Once released, open the lid and remove the chicken. Press Cancel on the Instant Pot to end the pressure cooking cycle.
Cut chicken into smaller, bite sized pieces and set aside. The Instant Pot should still contain the gravy.
In a small bowl, mix corn starch with 1/4 cup warm water. Set the Instant Pot to the Sauté setting Once the gravy begins to boil, add the corn starch mixture and stir vigorously.
Once the gravy begins to thicken, add the chicken back into the instant pot and mix. Add broccoli florets and mix.
Once everything has been coated in the gravy, cancel the Sauté setting and select Keep Warm. Replace the lid. This will allow the broccoli to cook in the steam for around 10 minutes.
Serve with white or brown rice.