Crisp bacon in a large Dutch oven over medium heat; transfer to a paper towel–lined plate.
Place flour in a shallow bowl. Seasonchicken with salt and pepper and dredge inflour. Working in batches, cook chicken, skinside down, in same pot over medium heatuntil deep golden brown and crisp (do notturn), 12–15 minutes.
Transfer to a plate.
Working in 2 batches, cook mushroomsin same pot, seasoning with salt and pepperand stirring occasionally, until brown, 5–8minutes.
Transfer to a bowl.
Add onion andgarlic to pot; cook, stirring occasionally, untilonion is soft and translucent, 5–8 minutes.
Add wine to pot; simmer until reduced byhalf, about 5 minutes.
Add chicken, bacon,thyme, bay leaves, and broth; season withsalt and pepper. Bring to a boil, reduceheat, and gently simmer, partially covered,skimming occasionally, until chicken is fallingoff the bone, 2–2 1/2 hours.
Add mushroomsand simmer until flavors meld, 10–15 minutes;season with salt and pepper.
Bring a medium pot of salted water to a boil.
Whisk flour,baking powder, nutmeg, pepper, and 3/4 teaspoonssalt in a medium bowl.
Whisk in eggs andmilk (batter will be slightly lumpy). Reduce heat until water is at a strong simmer. Dropteaspoonfuls of batter into water; cook untildumpling are cooked through and doubledin size, about 5 minutes.
Remove with slottedspoon; add to stew just before serving.
DO AHEAD: Stew (without dumplings) can bemade 3 days ahead.
