Preheat a large non-stick 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, parsley, salt and pepper. 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 cover with a lid and simmer until the chicken reaches an internal temperature of 160°F using a thermometer.
Remove the chicken from the pan and simmer the sauce over medium-high heat until it thickens to a smooth consistency. Taste and adjust the seasoning with salt or more lemon juice. (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 parsley and lemon slices. Serve with bread.
Notes
Pro tips: Butterfly the chicken: Lay the breasts down on a cutting board, using a sharp knife parallel to the cutting board slice the breasts through the middle (carefully) all the way in half.