Pour the water or chicken broth, honey, soy sauce, garlic, and pepper into the inner pot of your Instant Pot. Whisk until the honey is dissolved.
Add the chicken breasts to the pot, turning to coat them in the sauce.
Secure the lid, move the steam valve to the 'Sealing' position. Select the 'Pressure Cook' or 'Manual' setting on high pressure. Cook for 8 minutes for small breasts (7-8 oz), 10 minutes for medium (10 oz), or 11 minutes for large (12 oz).
Once the timer finishes, carefully perform a quick release by moving the steam valve to 'Venting'. Wait for the float valve to drop before opening the lid.
Check the internal temperature of the thickest part of the chicken with a meat thermometer. It must be at least 165°F (74°C).
Remove the chicken to a plate or cutting board and let it rest.
Select the 'Sauté' function. In a small bowl, whisk together the cornstarch and 1 tablespoon of cold water to make a slurry.
Once the sauce in the pot is bubbling, stir in the cornstarch slurry. Cook, stirring constantly, for 2-3 minutes until the sauce has thickened.
Slice the chicken against the grain. Serve immediately, topped with the thickened honey garlic sauce.