Preheat the insta-cooker by selecting sauté on high heat and add butter.
Season the chicken with salt and pepper and dredge in the flour, shaking off the access. Once the butter is sizzling and the pot is hot, add half of chicken in one later. Brown on one side for 3 or 4 minutes, without moving. Flip and brown the other side. Removed and repeat with remaining chicken, set aside.
Add the celery, carrots, and onions to the pot. Sauté for 3 minutes, scraping the bottom of the pot. Add the chicken and broth. Season with salt and pepper. Secure the lid
Select manual and cook at high pressure for 11 minutes.
To make the dumplings
While the chicken is cooking, make the dumplings. Mix together the flour, cornmeal, baking powder, salt, and pepper in a medium bowl. Add the milk or half and half and melted butter, stir until just incorporated (don't over mix)
Once cooking is complete use a quick release. Remove the chicken and set aside.
Add the milk to the broth in the pot, Mix and season with salt and pepper. In a small bowl, combine 1/2 cup hot broth with the cornstarch and whisk to combine. Add back into the pot
Select Sauté. Once simmering, scoop heaping tablespoons of dumpling mixture and drop them into the pot. Try to keep them separated and mostly submerged, without disturbing them too much
Reduce sauté heat to low and cook 12 to 15 minutes, loosely covered with the top without locking it, until the dumplings have doubled in size.
Meanwhile, bone the chicken, remove and discarded the skin, and shred the meat. Add back into the pot and serve.