Prepare the chicken: Place each chicken breast between two sheets of cling film or baking paper. Using a rolling pin or meat mallet, gently pound them to an even thickness of about 1cm. You should feel the fibres relaxing under the pressure, and the meat will look uniformly pale and slightly wider. Season both sides with a pinch of salt and pepper.

Set up the dredging station: In a shallow bowl, combine the flour with half a teaspoon of salt and a pinch of pepper. In a second bowl, whisk the eggs and milk together until the mixture is a uniform, pale yellow colour with no streaks of white — it should look like a smooth, thin custard and smell faintly of fresh eggs.

Coat the chicken: Take one chicken cutlet and dredge it first in the flour, shaking off any excess until you see a light, dusty coating. Then dip it into the egg mixture, letting any excess drip off for a second or two. The coating should look glossy and wet, but not clumpy. Place the coated cutlet on a wire rack and repeat with the remaining pieces. Let them rest for 5 minutes — you will see the coating begin to set and look tacky, which helps it stick during frying.

Fry the cutlets: In a large frying pan, heat 2 tablespoons of butter and 2 tablespoons of olive oil over medium-high heat. When the butter has melted and the foam subsides, the oil will shimmer and a pinch of flour dropped in will sizzle immediately. Carefully place two cutlets into the pan, ensuring they are not touching. Cook for 3 to 4 minutes per side, until the underside is a deep golden brown and you hear a steady, gentle hiss. Flip them using a spatula; the second side will take slightly less time. Transfer the cooked chicken to a warmed plate and repeat with the remaining butter and oil for the second batch.

Make the lemon sauce: Reduce the heat to medium. Pour out any excess oil from the pan, leaving about a tablespoon of the browned bits (the fond) stuck to the bottom. Add the chicken stock and lemon juice, then bring it to a gentle simmer while scraping the bottom of the pan with a wooden spoon. You will see the fond dissolve into the liquid, turning it a pale, speckled gold. Let it bubble for 2 minutes until it reduces slightly and smells fragrantly of lemon.

Finish the sauce: Whisk in the remaining 1 tablespoon of butter until it melts completely, creating a sauce that looks glossy and smooth, almost like a thin syrup. Stir in the lemon zest and capers, if using. The sauce should be tangy and aromatic, with a silky texture that coats the back of a spoon.

Combine and serve: Return the chicken cutlets to the pan, spooning the sauce over the tops. Let them warm through for 1 to 2 minutes, turning once so both sides are glistening. Sprinkle with fresh parsley just before serving. The chicken will be tender inside, the crust still slightly crisp on the edges, and the sauce will cling to every bite.