In a medium bowl, beat the eggs and add the cheese and parsley flakes. Put the flour in a shallow bowl.
Heat the vegetable oil and the olive oil in a skillet When oil is hot enough, dip the chicken in the flour, then the egg mixture, then the flour again. Fry the chicken until golden on both sides, turning once. Drain on paper towels and move to warm oven.
Discard the oil and add the chicken stock to the skillet. Bring to a boil and reduce by half, making sure to scrape up any browned bits left from the chicken.
Add the lemon juice then the butter, whisking constantly, until it is melted. Season with salt and white pepper.
Plate the chicken breasts and pour the sauce over. Garnish with the chopped parsley and lemon slices.