In a large pot, combine the chicken pieces, chicken broth, and water. Bring to a boil, then reduce the heat and let it simmer for about 30 minutes, skimming off any foam that rises to the surface.
Add the sliced carrots, leeks, celery, chopped onion, minced garlic, bay leaf, dried thyme, ground black pepper, and salt to the pot. Continue to simmer for another 20-30 minutes, or until the chicken and vegetables are tender.
Carefully remove the chicken pieces from the pot and let them cool slightly. Remove the meat from the bones, discarding the skin and bones. Shred or cut the chicken meat into bite-sized pieces and return it to the pot.
In a medium bowl, whisk together the heavy cream and egg yolks. Set aside.
In a small saucepan, melt the butter over medium heat. Stir in the flour to make a roux, cooking for about 1-2 minutes until lightly golden.
Gradually whisk the roux into the simmering pot of chicken and vegetables, stirring constantly to thicken the broth slightly.
Gradually add the cream and egg yolk mixture to the pot, stirring constantly to avoid curdling. Heat gently, but do not boil.
Adjust seasoning with additional salt and black pepper to taste.
Ladle the waterzooi into serving bowls.
Garnish with freshly chopped parsley.
Enjoy your meal!