1. Pat chicken thighs dry with paper towels and season with salt and pepper. Melt butter in Dutch oven over medium-high heat. Add chicken thighs, skin-side down, and cook until skin is deep golden brown, about 8 minutes. Transfer to slow cooker.
2. Pour off all but 1 tablespoon fat from pot. Cook carrots, celery, and onions until softened, about 5 minutes. Stir in garlic, thyme, and pepper flakes and cook until fragrant, about 30 seconds. Add 1 cup broth to pot and scrape up any browned bits with wooden spoon. Transfer vegetable mixture, bay leaves, and remaining broth to slow cooker.
Season chicken breasts with salt and pepper and wrap in foil according.
**Protecting Chicken Breasts: Wrapping the chicken breasts in a foil pack insulates the delicate white meat, helping keep it moist and tender. To make the foil pack, place the chicken on one side of a large piece of heavy-duty aluminum foil. Fold the foil over, shaping it into a packet that will fit into your slow cooker, then crimp to seal the edges. Place foil packet in slow cooker. Cover and cook on low until breasts are cooked through and thighs are tender, 4 to 4 1/2 hours.
4. Remove foil packet from slow cooker. Carefully open foil and transfer chicken breasts to plate. Remove chicken thighs from slow cooker and transfer to plate. When cool enough to handle, shred meat into bite-sized pieces, discarding skin, bones, and excess fat.
5. Stir shredded chicken, cooked noodles, peas, and parsley into slow cooker. Cover and cook until heated through, about 5 minutes. Discard bay leaves. Serve.