Combine the ingredients in the slow cooker. Place the chicken breasts or thighs into the bottom of a large slow cooker (6-quart or larger). Add the chopped onion, carrots, and celery around the chicken.

Pour in the chicken broth, cream of chicken soup, and cream of celery soup. Season the mixture with dried thyme, salt, and black pepper. If using butter, slice it into four pieces and place it on top of the mixture.

Cover and cook on LOW for 6 to 8 hours or on HIGH for 3 to 4 hours, until the chicken is very tender and easily shredded.

Shred the chicken. Carefully remove the cooked chicken from the slow cooker and place it on a cutting board. Use two forks to shred the chicken, then return the shredded meat back to the slow cooker and stir well.

Prepare the dumpling dough. While the slow cooker is heating up again (if needed), whisk together the flour, baking powder, and salt in a medium mixing bowl.

Pour in the milk and the melted butter. Stir gently until just combined. The dough will be slightly sticky and wet, similar to a thick biscuit dough. Do not overmix.

Drop the dumplings. Ensure the slow cooker mixture is actively simmering and hot. Using a tablespoon or small cookie scoop, drop the dumpling dough directly onto the surface of the chicken mixture. Leave a small space between each dumpling to allow for expansion.

Cook the dumplings. Cover the slow cooker immediately. Cook the dumplings on HIGH for 30 to 45 minutes, or until the dumplings are puffy, doubled in size, and cooked through. Avoid removing the lid during this time, as the steam is essential for cooking the dumplings properly.

Serve hot. Stir the mixture gently once the dumplings are cooked to incorporate them into the stew. Serve the Crock Pot Chicken & Dumplings immediately.