Bring 1/2 cup of the chicken stock to a boil and pour over the morels in a heatproof bowl. Soak for 1 hour, then drain, Reserve the liquid and chop fine.
Strain the soaking liquid through a coffee filter and set aside. Place each chicken breast half between two sheets of waxed paper and pound with the flat side of a meat pounder until thin.
In a small bowl, combine the ground chicken, egg, 1 tb of the parsley, the dill and 2 tbls of the chopped morels. Season with salt and pepper and mix well.
Place half of the filling along the long side of each breast half, tuck in the ends and roll up. Secure with a wooden toothpick.
Place the chicken rolls in a medium-sized saucepan and add the morel soaking liquid, the remaining broth, the wine and the remaining morels.
Bring the liquid to a boil, then reduce the heat to low, and partially cover, poaching the chicken until cooked through, 20 minutes.
With a slotted spoon, remove the chicken to a heated platter. Over medium-high heat, reduce the poaching liquid to 1/2 cup, 15 minutes.
Add the cream and cook for 7 minutes longer. Remove the pan from the heat and whisk the butter and the vermouth until well blended in the liquid.
Stir in the remaining parsley and season with salt and pepper to taste.