Prepare your mise en place: chop the onion, dice the carrots, slice the celery, and measure out the stock and chicken. If you’re using rotisserie chicken, shred it and set it aside so it’s ready to go when the pot comes together.
Set your Instant Pot to the Sauté function and add the olive oil. Once shimmering, add the onion, carrot, and celery. Cook for about 4–5 minutes, stirring occasionally, until the vegetables are softened and the onions are translucent. This builds the base flavor that will perfume the entire dish.
Pour in the chicken stock and add the bay leaf and thyme. Stir to combine, scraping up any browned bits from the bottom of the pot—this is where a lot of your savory depth comes from.
Add the shredded chicken and the peas (if using). Let the mixture come to a gentle simmer. Taste and adjust a pinch of salt if needed, keeping in mind the dumplings will contribute some floury density.
In a separate bowl, whisk together the flour, baking powder, and salt. Stir in the milk and melted butter until a thick, lumpy batter forms. Do not overmix; a few small lumps are perfectly fine and help create light dumplings.
Drop spoonfuls of the dumpling batter onto the simmering stew in even rounds. Space them apart but keep them on top of the liquid so they cook through. You should be able to fit about 8–10 dumplings depending on their size.
Seal the Instant Pot with the lid, set the valve to sealing, and cook on High Pressure for 5 minutes. After the timer goes off, do a quick release by carefully turning the valve to venting.
Open the pot and gently stir the dumplings and broth to blend the flavors. If the dumplings seem dense, you can simmer the pot on Sauté for a few minutes uncovered to help the broth reduce a bit and the dumplings finish firming up.
Taste once more and adjust with a bit of salt or pepper as desired. If you like a bit of brightness, a squeeze of lemon juice or a sprinkle of fresh parsley can brighten the finish just before serving.