Remove the rind from the bacon. Dice the bacon. Peel and cut up the potato and leeks. Slice the celery. Place the bacon and vegetables with the water in the saucepan. Season. Cover and simmer for 3 minutes.
Separate the egg yolk from the white and mix the yolk with the milk. Remove the saucepan from the heat and stir in the egg yolk and milk. Reheat for 2-3 minutes but do not boil. Serve sprinkled with parsley.