Set a frying or sauce pan over high heat. Add ½ cup of the cooking liquid from the chicken along with the butter and 1 tsp of kosher salt.
Bring to a boil.
Once boiling add all the flour at once. Stir with a wooden spoon until a dough comes together.
Reduce the heat to low and continue stirring for a couple more minutes or until the dough is in a ball and is no longer really sticky.
Place into a large mixing bowl and get out a hand mixer.
Using the mixer, mix the dough until it breaks into little balls and has cooled.
Add 1 egg at a time and mix it to combine. Make sure it's completely incorporated before adding the next egg.
Once you have incorporated the last egg, place the dough into a resalable plastic bag. Cut out a corner to make a piping bag.
HIt the saute button on the Instant Pot and bring your broth to a simmer. Squeeze the dough out of the corner of the bag, cutting the dough with kitchen shears at about 1 inch.
When you are finished, cook the dumplings for 8 to 10 minutes with the lid back on but not sealed. If the water starts to boil too hard, just hit the keep warm button or turn off the pot.
Once the dumplings are cooked through (check one), add in the chicken. Give the chicken a couple minutes to warm up then serve the soup.