-
1
Place chicken in a Dutch oven. Add water, carrot, celery, onion, 3 sprigs of thyme, and bay leaf. Bring to a boil, cover, reduce heat to low, and simmer for 1 hour. Remove chicken from dutch oven and transfer to a bowl; set aside to cool.
-
2
Increase heat and bring the stock to a simmer. Skim off any chicken fat that appears on top of the stock and reserve in a bowl. Combine 2 to 3 tablespoons of the reserved fat with flour in a small bowl; stir to make a paste, adding more flour if needed. Add the chicken fat and flour mixture to the stock. Reduce heat and simmer for 15 minutes.
-
3
Remove chicken meat from the carcass and add to the stock. Season with salt, black pepper, and cayenne pepper to taste. Continue simmering for 10 to 15 minutes.
-
4
Whisk creme fraiche, milk, 2 teaspoons of thyme leaves, and eggs together in a large bowl. Stir in self-rising flour until almost entirely incorporated; do not overmix.
-
5
Scoop large dollops of dumpling mixture on top of the chicken stock. Increase heat slightly to medium-high. Cover and simmer until dumplings appear light and fluffy, and a toothpick inserted into the center comes out clean, 10 to 15 minutes. Serve garnish with thyme sprigs.
