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1
For the stew: Place the chicken in the pot; arrange the dark meat pieces on the bottom and the split breast halves on top. Arrange the breasts so that they are nested together, skin-side down. Add 4 cups water, 2 tablespoons of the butter, thyme, and salt. Cover and cook on high pressure for 8 minutes. Let stand for natural release for 5 minutes, then quick release the remaining pressure.
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2
Transfer the chicken pieces to a plate. As soon as they are cool enough to handle, pull the meat from the bones and shred it into bite-size pieces. Save the skin and bones for step 3. Place the meat in a medium bowl, cover, and refrigerate it until needed.
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3
Return the bones and skin to the pot. Add the vinegar. Cover and cook on high pressure for 15 minutes. Quick release the pressure. Strain the stock through a fine-mesh sieve into a large bowl and set aside until needed. Discard the solids. Rinse and dry the pot and return it to the multicooker.
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4
Heat the remaining 1 tablespoon butter in the pot on saute medium. Add the onion, celery, carrots, and thyme and stir to coat. Cook until tender, about 5 minutes, stirring often. Stir in the reserved stock and chicken meat and season with salt and pepper. Cover with a tight-fitting tempered glass lid and select the keep warm setting.
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5
For the dumplings: Whisk together the flour, baking powder, salt, sugar, and pepper in a medium bowl. Work the butter and shortening into the flour with your fingertips until the mixture is crumbly. Slowly stir in enough half-and-half to make a soft, sticky dough that barely holds its shape on a spoon.
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6
Uncover the pot and bring the chicken stew to a gently bubbling low boil on saute low. (If the stew isn't warm enough to bubble, the dumplings will turn out dense and soggy. If the stew boils vigorously, the liquid will reduce too much.) Use a 1-ounce scoop or two spoons to drop dumplings the size of Ping-Pong balls evenly over the surface of the stew.
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7
Cover with a tight-fitting lid that can hold in the heat, preferably a tempered glass lid that lets you monitor the bubbling stew and see the dumplings while they cook. Simmer until the dumplings are firm and fluffy, 15 to 20 minutes. Uncover and let stand 5 minutes. Sprinkle with parsley and serve warm.
