Lay out the buttermilk in one dish and blend the flour, cheese, salt, pepper and lemon zest in another.
Soak the cutlets in the buttermilk while you prep the salad greens on dinner plates. Dress lightly with oil and vinegar.
Preheat a saute pan on medium heat, add 2 tbsp olive oil and 2 tbsp butter. When the butter is sizzling, dredge the cutlets one at a tme in the flour mixture and set into the pan. Brown the chicken on one side and flip until cooked through. This should only take a few minutes. Add the lemon juice towards the end of cooking.
Slice the cutlets into sections and place on top of the greens. Garnish with parsley and lemon zest. You can make the chicken ahead of time and serve cool if you don't want to heat your kitchen at dinnertime.