3 ½pounds bone-in chicken pieces, preferably dark meat
1 ½teaspoons kosher salt, plus more as needed
½teaspoon freshly ground black pepper
4tablespoons (1/2 stick) unsalted butter
2celery stalks, diced
1Spanish onion, diced
1turnip, peeled and diced
4garlic cloves, smashed
¼cup all-purpose flour
1quart chicken stock, preferably homemade
Chopped fresh parsley or celery leaves, for serving
For the dumplings
1 ½cups all-purpose flour
½cup fine cornmeal
¼cup minced fresh chive (optional)
2teaspoons baking powder
¾teaspoon kosher salt
¼teaspoon freshly ground black pepper
2tablespoons butter, melted
¾cup whole milk
In a large bowl, toss the chicken pieces with the salt and pepper. Let them sit for 20 minutes.
Using the sauté function, melt 2 tablespoons of the butter in the pressure cooker. Add the chicken pieces, in batches, and brown them on all sides until deep golden brown, about 5 minutes per side. Transfer the chicken to a plate.
Add the remaining 2 tablespoons butter to the pressure cooker and stir in the carrots, celery, onion, turnip, and garlic cloves. Cook until softened, about 10 minutes. Then stir in the flour and cook until the mixture starts to turn golden, about another 3 minutes. Stir in the chicken stock, scraping up the browned bits from the bottom of the pot, and nestle the browned chicken into the vegetables. Cover and cook on high pressure for 13 minutes, and then release the pressure manually. Transfer the chicken pieces to a plate, reserving the broth in the pot. When the chicken is cool enough to handle, remove the bones and skin if you like, and tear the meat into chunks.
Meanwhile, make the dumplings: In a medium bowl, whisk together the flour, cornmeal, chives if using, baking powder, salt, and pepper. Pour the melted butter and the milk into the flour mixture, and stir gently with a spoon or spatula until just combined. Drop spoonfuls of the batter into the broth in the pot, spacing them evenly across the surface. Cover and cook on high pressure for 10 minutes.
Test the dumplings by cutting into one and making sure it’s cooked all the way through. If not, turn the sauté function on and simmer the dumplings until they are done.
Stir the chicken back into the pot to warm it up, and serve it topped with parsley leaves.
If you’d rather use a slow cooker, add the stock plus 1/2 cup water, bring to a simmer, and cook on high until the chicken is tender, 3 to 4 hours. Transfer the chicken to a plate. Drop spoonfuls of the dumpling batter into the slow cooker, cover, and cook on high until cooked through, 1 1/2 to 2 hours, depending upon their size.