Place the chicken breasts in a pan with the vegetables and peppercorns and cover with water.
Bring gradually to the boil and simmer until the chicken is cooked all the way through - about 30 minutes.
Carefully remove the chicken breasts from the cooking liquid and keep them warm.
Strain the cooking liquid into a clean pan, discarding the cooked vegetables. Reserve about 450ml/16fl oz of the liquid.
Melt the butter in a separate pan and add the flour. Cook until the mixture forms a smooth paste which leaves the sides and base of pan cleanly.
Gradually add the reserved cooking liquid to the mixture, a ladle at a time, allowing to boil after each addition before beating well. Stir until the mixture blends smoothly.
Pour the white wine into the sauce and reduce the heat to low.
In a small bowl, combine the egg yolk with the double cream. Stir the egg and cream into the sauce.
Add a squeeze of lemon juice and salt and freshly ground black pepper to taste.
Cut the cooked chicken into bite-sized pieces and stir into the sauce.
Garnish with chopped fresh parsley and serve at once.