Step 1: In a large pot or Dutch oven, combine the whole chicken, 4 cups chicken broth, 4 cups water, 2 tsp salt, 1 tsp pepper, 1 tsp garlic powder, and 1 bay leaf. Bring to a boil, then reduce heat, cover, and simmer for 1 to 1.5 hours, or until the chicken is very tender and cooked through.
Step 2: Carefully remove the chicken from the pot and set aside to cool slightly. Strain the broth through a fine-mesh sieve into a separate bowl, discarding solids. Once cool enough to handle, shred the chicken meat from the bones, discarding skin and bones.
Step 3: In the same pot, melt ½ cup butter over medium heat. Add diced celery, carrots, and onion. Sauté for 8-10 minutes until vegetables are softened. Stir in ½ cup flour and cook for 1-2 minutes, stirring constantly, to create a roux.
Step 4: Gradually whisk the strained chicken broth into the roux, a little at a time, until smooth and no lumps remain. Bring the mixture to a gentle simmer, stirring frequently, until the broth thickens to a creamy consistency. Return the shredded chicken to the pot and keep warm.
Step 5: To prepare the dumplings: In a medium bowl, whisk together 3 cups flour, 2 tbsp baking powder, 1 tsp salt, ¼ tsp pepper, and ¼ tsp thyme. In a separate bowl, combine 1⅛ cups chilled milk and 6 tbsp melted butter. Pour the wet ingredients into the dry ingredients and mix with a spoon just until combined; do not overmix.
Step 6: Drop spoonfuls of the dumpling dough (about 1.5-2 tablespoons each) directly into the simmering chicken and broth mixture. Ensure they are submerged. Cover the pot tightly and cook for exactly 10 minutes without lifting the lid. This allows the dumplings to steam and become fluffy.
Step 7: Remove from heat and let sit for 2-3 minutes before serving. Ladle into bowls and enjoy your comforting homemade chicken and dumplings!