Chicken and Dropped Dumplings

Steps

1. 1Put the chicken and 3 teaspoons of the salt in a 7-quart pressure cooker. Add enough water just to cover the chicken; do not fill above the cooker's "maximum fill" line, or 2/3 full. Cover and lock the lid. Bring to pressure over high heat, about 20 minutes.
2. 2Once the pot reaches pressure, reduce heat to low, so that you barely hear hissing from the pot. Cook for 45 minutes.
3. 3Following the manufacturer's instructions, release the pressure using the cooker's release device, or cool the cooker by running cold water over the lid for 5 minutes. Open carefully. Remove the chicken from the broth and set aside to cool. The meat should be tender and falling away from the bone. Once the chicken is cool enough to handle, pull the meat from the bones in small pieces, cover, and set aside. Discard the skin and bones.
4. 4Set a cheesecloth-lined colander in a shallow, wide, 6-quart pot, and strain the broth, discarding the solids. Taste and season the broth with additional salt, if desired.
5. 5Put 1/2 cup of the broth, the butter, and the remaining 1/2 teaspoon of salt in a 2-quart saucier, set over high heat, and bring to a boil. As soon as it boils, add all of the flour at once and stir with a wooden spoon until the mixture starts to come together, about 1 minute. Decrease heat to low and continue stirring until the mixture forms a ball and is no longer sticky, about 3 minutes. Transfer the mixture to a medium bowl and mix with an electric hand mixer, on low speed, until mixture is cool and there is no more steam rising, about 5 minutes. Continue to mix on low, and add the eggs, one at a time, making sure each is completely incorporated before adding another. You may need to stop occasionally and scrape down the sides of the bowl. Before adding the last egg, check the mixture for consistency: It should tear slightly as it falls from the beater, creating a "V" shape. Transfer the dough to a 1-gallon zip-top bag. Cut off 1 corner of the bag to make a quarter-sized opening.
6. 6Bring the broth to a slight simmer over medium heat. Pipe 1 inch of the mixture and cut with kitchen shears directly over the broth. Repeat with the remaining batter. Cook, covered, until the dumplings are cooked through, 8 to 10 minutes. Turn off the heat, add the meat, and wait for 2 to 3 minutes before serving. Serve in bowls with freshly ground black pepper.