Slice 450g of boneless skinless chicken breast into cutlets and pound to ¼in / 5mm thick. Coat with ½ tablespoon of olive oil.
Mix 4 tablespoons of all-purpose flour, 2½ tablespoons of finely grated Parmesan, ½ teaspoon of salt, and ¼ teaspoon of black pepper. Coat the chicken and shake off excess.
Heat 2 tablespoons of olive oil and 15g of butter in a large skillet over medium-high heat. Fry the chicken in batches for 3-4 minutes on the first side and about 1 minute on the second, until golden and 165°F / 74°C inside. Remove.
Discard excess fat and give the pan a quick wipe, leaving the browned bits. Add ⅔ cup of dry white wine and simmer for about 3 minutes, until reduced by half.
Add 2 tablespoons of lemon juice and simmer for 1 minute. Reduce the heat to low and swirl in 30g of cubed butter until glossy.
Stir in 3 tablespoons of drained capers and 1½ teaspoons of chopped parsley. Spoon over the chicken.