Prepare the Stew
Begin by melting the butter in a microwave-safe cup or measuring jug. Gradually stir in the flour until the mixture is smooth and free of lumps.
Cook the Stew
In the bowl of a 6- to 8-quart slow cooker, combine the butter-flour mixture with the chicken thighs, garlic, celery, carrots, onion, lemon juice, bay leaves, tomato paste, thyme, rosemary, chicken broth, and salt and pepper to taste. Stir well to combine. Cover and cook on the low setting for about 5 hours, or until the chicken and vegetables are tender.
Prepare the Dumplings
In a medium bowl, mix together the flour, cornmeal, baking powder, and salt. Add the buttermilk and melted butter, stirring until just combined. Be careful not to overmix, as this can affect the texture of the dumplings.
Add the Dumplings
After opening the slow cooker lid, use two forks to shred the chicken into bite-sized pieces. Using a large spoon or a ¼-cup measure, scoop the dumpling batter and drop it in dollops on top of the stew. Space the dumplings out, but don’t worry too much about their shape, as they will expand as they cook. Cover the slow cooker again and continue cooking on low for an additional hour.
Final Cooking
Once the dumplings are puffed up, remove the lid and allow them to cook uncovered for 15 more minutes. This will help firm up the tops of the dumplings. Serve the dish with a sprinkle of fresh parsley.