Chef John's Chicken and Biscuits

Place the chicken in a large, heavy pot with a tight-fitting lid. Add water and add sliced carrots, chopped celery, and diced onion to the pot as well. Include 3 sprigs of fresh thyme and a bay leaf for added flavor. Bring the mixture to a rolling boil, then cover the pot and reduce the heat to a low simmer. Allow it to cook for 1 hour, undisturbed.

Next, increase the heat and bring the stock to a gentle simmer. Carefully skim off any excess fat that rises to the surface of the stock and transfer it to a separate container. In another small bowl, combine 2 to 3 tablespoons of the reserved fat with a spoonful of flour. Mix until you have a smooth, thick paste; if needed, add more flour to achieve the desired consistency. Gradually stir in the chicken fat and flour mixture into the stock, then reduce the heat and simmer for 15 minutes.

Remove the chicken meat from its bones and add it back into the stock. Season with salt, black pepper, and a pinch of cayenne pepper to taste. Continue to simmer the mixture for 10 to 15 minutes, allowing all the flavors to meld together.

In a separate large bowl, whisk together creme fraiche, milk, 2 teaspoons of fresh thyme leaves, and eggs until well combined. Stir in self-rising flour until it is almost fully incorporated; avoid overmixing the mixture.

Using a spoon, scoop out large dollops of the dumpling mixture and place them on top of the chicken stock. Increase the heat slightly to medium-high, then cover the pot and simmer until the dumplings appear light and fluffy, and a toothpick inserted into the center comes out clean, 10 to 15 minutes. Serve hot, garnished with a few sprigs of fresh thyme.