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 the optional 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. Increase the setting to HIGH to prepare for the dumplings.

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

Pour in the milk (or buttermilk) 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 (on HIGH setting). 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. It is critical to avoid removing the lid during this time, as the trapped steam is essential for cooking the dumplings properly.

Serve hot. Once cooked, stir the mixture gently to incorporate the dumplings into the stew. Taste and add additional salt or pepper if needed. Serve the Crock Pot Chicken & Dumplings immediately.