Season the chicken pieces with salt and black pepper on all sides.

Melt butter in a large, heavy Dutch oven over medium heat. 

Add the chicken pieces in a single layer (work in batches if needed so you don’t overcrowd the pot) and cook, turning once, until pale golden, about 3-5 minutes per side. Remove the chicken to a plate and repeat with remaining chicken pieces, removing them once finished to the plate.

To the pan, add the chopped onions and sauté for 5 minutes, until softened. Stir in the flour and cook, stirring, for 1 minute.

Add the water and chicken stock, scrape the bottom of the pan to loosen any cooked on bits, and crank the heat up to high. Bring the mixture to a boil then add the mushrooms, carrots, celery, salt, pepper and thyme. Return the chicken pieces to the pot, along with any accumulated juices, and bring to a simmer. Reduce the heat to maintain a gentle simmer (just barely bubbling). It may not seem like enough liquid, but it will be.

Simmer, covered, until the chicken pieces are nearly cooked through, about 20 minutes. Skim any excess fat from around the sides of the pan with a spoon.

Meanwhile, make the dumplings. In a medium bowl, mix together the flour, baking powder and salt. 

Warm the milk and butter in a small saucepan until just simmering. Add the liquid to the bowl and use a fork or knead with your hands until the dough just comes together. Divide the dough into about 12-15 small dumplings. Roll each piece into a rough ball shape. Gently place the dumplings on the surface of the simmering chicken stew in the Dutch oven.

Cover and simmer for an additional 10 minutes, until a toothpick inserted in the dumplings comes out clean and the chicken is cooked through.

Serve immediately.