In a Dutch oven or a large kettle put the chicken, stock, salt, thyme, and bay leaf, cover and simmer for 45 minutes. Add the onions and carrots continue to simmer for an additional 10 minutes.
Remove 2 cups (500 ml) of liquid. Melt the butter in a small sauce pan, add the flour and cook for 2 minutes over low heat, (do not brown it). Slowly add the 2 cups of liquid stirring until thicken.
Whisk the lemon juice in the egg yolks. Blend into the sauce. Reheat but do not boil the sauce as this will curdle the eggs. Blend the sauce with the chicken. Stir in the cayenne. Pour into a serving bowl.
Sprinkle with parsley and serve over noodles or rice.