Using mallet, lightly pound chicken between sheets of plastic wrap to 1/2-inch thickness. Season chicken with salt & pepper.
Melt butter in heavy large skillet over medium-high heat. Add chicken to skillet and saute just until cooked through, about 3 minutes per side. Transfer chicken to platter; cover with foil and keep warm.
Pour butter from skillet. Add vermouth, lemon juice and lemon peel to same skillet; boil 1 minute, scraping up brown bits.
Add cream, broth and any juices accumulated from chicken; boil until reduced to sauce consistency, about 8 minutes.
Mix in 1/4 cup Parmesan. Season sauce with salt and pepper.
Pour sauce around chicken. Sprinkle with remaining Parmesan and parsley. Garnish with lemon if desired.