Preheat a large nonstick pan over medium heat with olive oil.
Season the chicken with salt and pepper. Dip the chicken into the flour to coat well and shake off excess.
Lightly beat the egg in a shallow bowl along with the parmesan cheese and 1/2 of the parsley. Dip the flour-coated chicken into the egg to coat both sides well, then into the pan.
Cook for about 3 minutes. When chicken is golden brown on one side, flip and cook the other side for about 3 minutes. Remove the chicken and transfer to a plate.
In the same pan melt the butter. Mix in 1 - 2 teaspoons of flour and cook for 1 minute while stirring together. Add the broth and lemon juice. Return the chicken to the pan and simmer for 5 minutes while stirring occasionally until the sauce thickens to a smooth consistency. (If the sauce is too thick, thin it out with a little more broth, if too thin, continue simmering until it reduces to a creamy consistency.) Garnish with remaining parsley. Serve with dinner rolls.