Slice the chicken breasts into cutlets. If they are thick, gently pound them until they are even. Season both sides with salt and pepper.

Put flour in one shallow bowl. In another bowl, beat the eggs with a pinch of salt, pepper, and Parmesan if using.

Warm a large skillet over medium heat. Add olive oil and 1 tablespoon butter. Let it melt without smoking.

Dredge each cutlet in flour, shake off the extra, then dip into the egg. Cook in the skillet for 3 to 4 minutes on each side until golden.

Move cooked chicken to a plate.

Lower the heat, add broth, and scrape up browned bits. Simmer for a minute, then add lemon juice and simmer for another minute.

Turn off the heat and stir in the remaining butter to make the sauce glossy.

Return the chicken to the skillet for 30 seconds to soak up the sauce, and serve garnished with parsley if desired.