Cut each chicken breast in half horizontally to form 4 thin steaks total.

Whisk the eggs and milk together in a small bowl and set aside.

Mix flour, salt, and pepper on a flat plate. Coat each chicken piece in the flour, shaking off the excess, then set aside on a clean plate.

Heat the olive oil in a large nonstick pan over medium-high heat until shimmering.

Dip each cutlet in the egg mixture, allow the excess to drip off, then place into the hot pan. Cook for 3 minutes until golden. Flip, reduce heat to medium, and cook for 4 more minutes until cooked through (internal temp 155 degrees F). Remove onto a plate.

Add the lemon slices to the same pan. Cook for about 1 minute until softened or lightly browned, then flip and cook the other side for 30 seconds. Remove onto a plate.

Wipe the pan clean using paper towels to remove the black bits.

Still on medium heat, melt the butter in the pan. Add flour and stir for 1 minute with a wooden spoon. While stirring, slowly pour in half the chicken stock. Once dissolved, stir in the remaining stock, wine, and salt.

Raise the heat slightly and simmer for 3 to 4 minutes, stirring occasionally, until the sauce thickens to a maple syrup-like consistency.

Return the chicken and lemon slices to the pan. Spoon the sauce generously all over the chicken and simmer for 30 seconds to warm through. Sprinkle with parsley and serve immediately.