Step 1

Place 1/2 cup of the flour, 1 teaspoon of the salt, and the pepper in a wide, shallow bowl and whisk to combine. Whisk the eggs and water together in a separate wide, shallow bowl.

Step 2

Heat the oil in a 10-inch or larger skillet over medium-high heat until shimmering. Dredge the cutlets in the flour, fully coating both sides and shaking off any excess. (You may have to cook the chicken in batches to avoid crowding the pan.)

Step 3

Coat the cutlets with the egg mixture. Let any excess drip off and add to the skillet. Cook until lightly browned, about 3 minutes per side. Transfer the chicken to a paper towel-lined plate. Repeat with any remaining cutlets if needed.

Step 4

Pour off and discard the oil in the skillet. Add the lemon slices to the skillet and cook until fragrant, about 30 seconds. Add the wine, broth, lemon juice, and remaining 1/2 teaspoon of salt. Simmer until slightly reduced, about 5 minutes. Meanwhile, use your fingers to rub the remaining 1 tablespoon of flour into the butter in a small bowl to make a paste.

Step 5

Add the paste to the sauce and whisk constantly until melted. Return the chicken to the skillet and cook until the sauce is thickened and the chicken is heated through, 3 to 4 minutes. Garnish with the parsley before serving.