In medium bowl, combine Parmesan cheese, prosciutto ham, raisins, dates, currants, shallots and garlic. Mix well.
With fingers, gently loosen skin from chicken breasts to form a pocket. Place 1 quarter of the mixture under the skin (into the pocket) of each chicken breast. Place chicken, skin-side-up, in roasting pan; pour stock around chicken breasts. Sprinkle with salt and pepper. Place in preheated oven and bake until cooked throughout, about 55 – 60 minutes.
Remove chicken breasts from pan and keep warm. Strain broth and drippings into a medium size bowl. Place small saucepan over high heat; add Vermouth. Bring to a boil; cook about 2 minutes to reduce. Add strained stock, bring to a boil and reduce another 5 – 8 minutes, or until liquid is reduced by half. Lower heat and slowly whisk in butter, adjusting heat so that sauce doesn’t boil. When butter has melted, plate chicken, spoon some sauce over breasts and serve immediately. Pass remainder of sauce separately.