Slice each chicken breast in half horizontally to create four thin fillets of even thickness.

In a shallow bowl, beat the eggs with the milk until well combined. Set aside.

On a plate, combine the flour, salt, and pepper. Dredge each piece of chicken in the flour mixture, shaking off any excess, and place them on a separate plate.

Warm the olive oil in a large non-stick skillet over medium-high heat. Dip each floured chicken fillet into the egg mixture, allowing the excess to drip off before placing it in the hot pan.

Sear the chicken for about 3 minutes on the first side until golden brown. Flip, reduce heat to medium, and cook for another 4 minutes or until the internal temperature reaches 68°C (155°F). Transfer the cooked chicken to a plate and set aside.

Add the lemon slices to the same pan. Let them cook for about 1 minute until they soften and take on a light brown color. Flip and cook for another 30 seconds. Remove the lemon slices and set aside.

Wipe the skillet clean using paper towels. Keeping the heat at medium, melt the butter in the pan. Stir in the flour and cook for 1 minute, using a wooden spoon to prevent burning.

Slowly pour in half of the chicken stock while stirring constantly, dissolving the flour into the liquid. Once smooth, add the remaining broth along with the white wine and salt. Stir continuously to maintain a smooth texture.

Increase the heat slightly and allow the sauce to simmer for 3 to 4 minutes, or until it thickens into a glossy, syrup-like consistency.

Return the chicken and lemon slices to the pan, coating them with the velvety sauce. Spoon the sauce generously over the top. Garnish with chopped parsley, and serve immediately with every bit of that luscious sauce.