FOR THE STEW: Pat chicken dry season with salt and pepper. Heat 1 tablespoon oil in cast iron skillet over medium-high heat until just smoking. Brown chicken all over and transfer to slow cooker.

Heat remaining 1 tablespoon oil in now-empty skillet over medium-high heat until shimmering. Add onions, celery, and carrots and cook until soft, 8 to 10 minutes. Stir in garlic, tomato paste, bay leaves, and thyme and cook until fragrant and tomato paste is starting to brown, about 2 minutes.

Stir in flour and cook for 1 minute. Slowly whisk in wine, scraping up any browned bits. Whisk in 1 cup broth and bring to simmer; transfer to slow cooker. Stir remaining 3 cups broth into slow cooker. Cover and cook until chicken is tender, 4 to 6 hours on low. Stir in peas.

FOR THE DUMPLINGS: 40 minutes before chicken is to finish, whisk flour, baking powder, and salt together in large bowl. Stir in milk and melted butter until just incorporated. Using greased 1/4-cup measure, drop 8 dumplings around perimeter of stew. Cover and cook until dumplings have doubled in size, 30 to 35 minutes. Remove bay leaves and serve.