1. Slice cleaned leeks into 1/2" slices. Melt butter in a large skillet and add leeks, carrots, and celery, cook until lightly browned.
2. Add all but 2 cups of chicken broth from the boiled chicken to the skillet.
3. Add the chicken breast cut up into small cubes.
4. Cover and simmer for approx 2 hours.
5. In the 2 cups of chicken broth you saved add the egg yolk to it and mix well. Add this to the skillet and continue cooking for another 3 mins.