Turn Instant Pot on and activate saute mode. Melt the butter in the pot.
Add onions and stir until they begin to soften (about 2-3 minutes).
Add carrots, celery, and potatoes. Stir.
Turn off the Instant Pot. Stir in parsley, paprika, and garlic powder.
Add the chicken breasts on top of the vegetables.
Add the stock. It's OK if the stock doesn't cover everything completely.
Place lid on the Instant Pot and lock into place. Set the steam release valve to the sealed position. Follow the instructions for your Instant Pot model to pressure cook on high for 5 minutes. The Instant Pot will take a few minutes to come to pressure, and then it will pressure cook for the 5 minutes and beep when it's done.
Once the pressure cooking has finished, let it sit with the lid on for 10 minutes. Then release the pressure by turning the pressure valve to the vent setting.
Remove the chicken and shred the meat using two forks. Set aside.
Combine the cornstarch and cold water. Turn on the saute setting and stir in the cornstarch and water mixture. This will help the soup thicken. Stir while it thickens, about 2-4 minutes.
Stir in the frozen peas, chicken, and heavy cream. Continue to cook for a few more minutes, stirring frequently. Turn off the Instant Pot. Add salt and pepper to taste.
Cooking time includes time for the Instant Pot to come to pressure, the pressure cooking time, the 10 minutes resting/natural release time, and the active cooking time (sauteeing the vegetables and thickening the soup).