Have the meat cutter remove the tendon from turkey breast and cut into scaloppine (thin slices). Season turkey slices with salt and pepper. Dredge in flour, shaking off excess; set aside. Heat oil and 4 tablespoons of butter in large skillet over medium-high heat. Add turkey slices and sauté (in batches, if necessary) until golden brown and no longer pink in center; about 1-2 minutes per side. Transfer to serving platter and keep warm. Repeat with remaining turkey slices.
Pour vermouth and lemon juice into skillet, scraping up browned bits. Bring to a boil and cook over high heat until slightly reduced, about 3-4 minutes. Pour any accumulated turkey juices from platter into skillet. Reduce heat to low and stir in remaining 2 tablespoons butter. Pour lemon sauce over turkey slices and garnish with parsley, Parmesan and lemon zest, if desired.