Set the Instant Pot to sauté, by pushing the sauté button until it shows sauté "MORE." Add olive oil to the pot. Sprinkle all-purpose seasoning over all sides of the chicken thighs.
When the pot is ready to sauté, brown the chicken thighs on all sides until lightly golden, about 5 minutes total.
Remove the boneless thighs and let rest on a plate. Add the broth to the pot and stir to deglaze the pan.
Return the chicken to the Instant Pot. Add the cherry tomatoes. Press the cancel button. Twist on the Instant Pot lid, turn the pressure lever to seal (if needed), then press the high-pressure button and set for 6 minutes.
When pressure cooking is complete, do a natural release for 10 minutes (let the pot rest undisturbed), then perform a quick release (turn or depress the pressure valve).
Transfer chicken and cherry tomatoes to a serving platter and cover loosely with foil.
Prepare the creamy pesto sauce
Drain the chicken broth from the pot, reserving 1/2 cup in the pot. Leave the pressure cooker warm, and stir in the pesto sauce and cream cheese. Continue stirring (I recommend using a whisk) until the two combine and are smooth. Add reserved chicken broth, as needed to make a smooth, creamy pesto sauce.
To serve
For serving, add a mozzarella slice to the top of each chicken thigh, spoon over the creamy pesto sauce, then top with cherry tomatoes. Sprinkle with fresh basil (optional) to garnish.
Notes
To use frozen chicken thighs, skip searing and add 2 minutes to pressure cooking.To use other cuts of chicken:
for boneless chicken breasts, pressure cook for 10 minutes
for chicken tenderloins, pressure cook for 4 minutes
for large, bone-in half breasts, pressure cook for 12 minutes
Leftovers will last for up to 4 days in the refrigerator. Let everything cool completely and transfer to individual airtight containers before placing them in the fridge.