Prepare the Chicken: Season the chicken quarters generously with salt, black pepper, garlic powder, and paprika on both sides. In a large cast-iron skillet, melt the butter with the olive oil over medium heat. Place the chicken skin-side down in the skillet and sear for about 5 minutes until golden brown. Flip the chicken and cook for another 3 minutes.
Simmer the Chicken: Transfer the browned chicken to a large stockpot and pour in 10 cups of water, leaving the butter and oil in the skillet. Bring the water to a boil, then skim off any foam from the surface. Reduce the heat and let it simmer, partially covered, for 30 minutes. Remove the chicken breasts from the pot and continue simmering the rest of the chicken for another 30 minutes.
Cook the Vegetables: While the chicken is simmering, heat the skillet with the reserved butter and drippings over medium heat. Add the chopped onion, carrots, and celery, seasoning with salt and pepper. Sauté for about 5 minutes, or until the vegetables start to soften. Stir in the minced garlic, fresh thyme, sage, and bay leaves, cooking for another minute until fragrant.
Combine the Flavors: Transfer the cooked vegetables to the pot with the simmering chicken. Pour the remaining 1 cup of water into the skillet, scraping up any browned bits from the bottom, then add this liquid to the stockpot. Let the mixture simmer for an additional 10 minutes until the chicken is tender and easily pulls apart. Remove the chicken from the pot, shred it with a fork, and set it aside.
Make the Dumpling Dough: While the soup continues simmering, melt the butter in a small microwave-safe dish, then mix in the minced garlic. In a large mixing bowl, whisk together the flour, baking powder, and salt. Beat in the egg, then gradually stir in the buttermilk and the melted garlic butter, mixing until a soft dough forms.
Finish the Soup: Return the shredded chicken to the pot and stir in the heavy cream. Bring the soup to a gentle simmer.
Cook the Dumplings: Using a spoon, drop small dollops of the dumpling dough into the pot. Cover and let them cook over low heat for about 5 minutes, or until the dumplings are fully cooked and fluffy.
Serve: Remove the bay leaves, ladle the soup into bowls, and top with fresh chopped parsley. Serve hot and enjoy this delicious soul food comfort dish!