Sauté the chopped morel mushrooms in the three tablespoons of butter until they've started to soften.
Preheat the oven to about 200 F.The oven will be used to keep the cooked chicken breasts warm.
Using a large saucepan, bring the white wine to a simmer, then add the chicken breasts with the salt and pepper. Bring back to a simmer, cover, and continue to simmer for about 15 minutes.
Remove the chicken from the liquid, cover with foil, and place it in the preheated oven.
Boil the cooking liquid uncovered until it reduces by about half. Add the sautéed mushrooms as well as the sliced fresh morels at this time. After adding the mushrooms, remove the pan from the heat.
In a small bowl, beat the egg yolks and cream with a whisk. Add two or three tablespoons of the hot cooking liquid to the egg and cream mixture and continue to whisk.
When thoroughly combined, add the egg and cream mixture to the cooking liquid in the saucepan.
Cook the wine, egg, mushroom, and cream mixture over a low heat, whisking constantly. Continue cooking gently until thickened, but be very careful not to permit it to come to a boil or it will coagulate.
When it thickens, stir in the minced parsley, and pour the piping hot sauce over the chicken and serve.