Cover chicken breasts with plastic wrap and pound them down with a meat pounder until they are evenly thin.
Dip the chicken in flour and shake slightly to remove the excess.
Heat butter and olive oil in a large pan over medium-high heat. Once the oil and butter are hot, add the chicken breasts, letting them cook on each side until they are brown and crispy and cooked through.
Remove the chicken and set aside on a plate. (You may have to cook the chicken in waves, depending on how flat it got.)
Whisk in some flour with the leftover oil and butter, then pour in the freshly squeezed lemon juice and chicken broth.
Reduce the heat to a simmer and add the chicken back in. Let the chicken simmer until the sauce becomes thick. Season everything with salt and pepper.
Serve the chicken over rice with fresh lemon wedges and garnish with chopped parsley.
