In a bowl, season chicken with salt and pepper to personal preference. Then add 2 tbsp pesto into the bowl and mix to coat.
Turn your Instant Pot (or other Pressure Cooker) to the Sauté setting. Coat the bottom of the pot with olive oil. Add chicken into the pot and allow to brown, about 4 minutes. Use tongs to flip the chicken thighs, browning on the other side as well. Do not cook all the way through, but allow the outside to brown. Remove thighs and place on a separate plate.
With the saute setting still on, add the chicken broth into the pot to deglaze. Use a wooden spoon to scrape up any chicken bits stuck to the bottom of the pot.
Add ½ cup pesto and ½ cup cherry tomatoes into the pot, then add chicken thighs back in. Turn off saute.
Close the pressure cooker and seal. Cook on Manual for 6 minutes. When complete, allow a Natural Release for 5 minutes, and then use an instant release to release the rest of the pressure.
Open the lid. Quickly place a slice of mozzarella cheese on top of each chicken thigh. Then, close the lid to the pot and seal again (but do NOT turn on the pressure cooker). Allow to sit for 2-3 minutes until the residual heat melts the cheese slices.
Remove the lid and serve with pasta or potatoes. Enjoy!