Turn your Instant Pot to the sauté setting and let it heat up for a minute. Add the butter and let it melt completely, swirling it around the bottom of the pot.
Add the diced onion, sliced carrots, and sliced celery. Cook for 4 to 5 minutes, stirring occasionally, until the onion turns soft and slightly translucent. Add the minced garlic and cook for another 30 seconds, just until fragrant.
Add the chunks of chicken thighs directly on top of the sautéed vegetables. Sprinkle the poultry seasoning, dried thyme, salt, and black pepper evenly over the chicken.
Pour in the chicken bone broth, making sure to scrape up any browned bits stuck to the bottom of the pot with your wooden spoon. Stir in the cream of chicken soup until it is mostly dissolved into the broth.
Secure the lid on your Instant Pot and turn the valve to the sealing position. Set the pot to manual or pressure cook on high for 10 minutes.
Once the cooking cycle ends, let the pressure release naturally for 10 minutes. After 10 minutes, carefully turn the valve to venting to release any remaining pressure. Remove the lid once the pin has dropped completely.
Turn the Instant Pot back to the sauté setting so the liquid returns to a gentle simmer. Cut the refrigerated biscuit dough into quarters, so each biscuit becomes four smaller pieces.
Drop the biscuit pieces on top of the simmering stew in a single layer, without stirring them in. Close the lid loosely, or use a splatter screen, and let the dumplings steam for 8 to 10 minutes. Check that a dumpling is cooked through by cutting one in half — it should look fluffy inside, not doughy.
Gently push the dumplings to one side of the pot to expose some of the liquid underneath. Stir the cornstarch and cold water mixture until smooth, then pour it into the exposed liquid.
Stir very gently to avoid breaking apart the dumplings, letting the stew thicken for 1 to 2 minutes. Pour in the heavy cream and the frozen peas, stirring gently just until everything is warmed through.
Turn off the Instant Pot and let the stew sit for a couple of minutes to thicken further before serving.
Ladle the chicken, vegetables, and dumplings into bowls, making sure everyone gets a good mix of both. Sprinkle chopped fresh parsley over the top for a pop of color.
Serve immediately while everything is warm and the dumplings are at their fluffiest.