Pat the chicken dry and, if necessary, slice each piece horizontally to make thin cutlets.

Whisk the eggs with the milk, 1 teaspoon of kosher salt, and 1/2 teaspoon of pepper. Measure the flour and put it in a wide shallow bowl or on a plate.

Dip the chicken in the flour and then coat with the egg mixture.

Heat the oil in a large, deep skillet or sauté pan over medium heat.

When the oil is shimmering, add the chicken pieces. Lower the heat to medium-low and cook the chicken for about 3 to 4 minutes on each side, or until nicely browned. Remove the chicken to paper towels to drain. To avoid crowding, you might have to cook the chicken in two batches.

Pour off the oil and wipe out the pan.

Place the pan over medium heat and add the butter, wine, and 2 tablespoons of lemon juice. Bring to a boil and continue to cook for about 4 minutes. Add the chicken stock and boil for about 5 minutes. Taste and adjust the seasonings with more lemon juice, salt, and pepper, as needed.

Add the chicken back to the sauce mixture and cook for about 5 minutes, or until hot and the chicken is thoroughly cooked.

For a thicker sauce combine the cornstarch with water and add it to the sauce about 1 to 2 minutes before it is done.

Arrange the chicken in a serving bowl or on a platter. Drizzle with the sauce and sprinkle with chopped parsley.