Dice the celery, onion, carrots, and potatoes; mince garlic. When about halfway through dicing the veggies, press the “sauté” function on the Instant Pot. Add butter and the veggies as you finish dicing them. Continue to sauté, stirring occasionally, until all the veggies are in, then turn off the sauté function.
Add remaining ingredients EXCEPT biscuit, cream, and peas. Make sure the chicken is submerged in the liquid and arranged in a single layer.
Cut each of the buttermilk biscuits into eight pieces. Gently place these pieces on top of the other ingredients in the Instant Pot, ensuring an even layer. Do not press down.
Seal the Instant Pot and use manual mode to cook on high pressure for 9 minutes. Once done, use the quick-release function to stop the cooking. Carefully remove the lid.
Gently move biscuits to one side in the pot. Using a slotted spoon, transfer the chicken thighs to a cutting board. Dice or shred the chicken, discarding the fat.
After taking out the chicken, add the heavy cream and peas to the Instant Pot. Stir gently. Place the lid back on the pot for a few minutes while working on the chicken. Add the diced or shredded chicken back in, stir, and add additional parsley if desired.
Taste the dish and adjust the seasoning if necessary. Ladle the chicken and dumplings into bowls and serve hot. Enjoy!