Rinse and pat dry chicken. Pound the chicken breast halves until more or less flat and even looking. Or you can use chicken cutlets instead.
Mix together salt, black pepper, flour, and parmesan in a shallow dish. Toss the pieces of chicken in the mixture until fully coated.
Heat 3 tablespoon cooking oil and 3 tablespoon butter in a pan over medium-high heat. Once the butter melted, cook the chicken on both sides for 3-4 minutes per side. If needed, do it in batches, and don’t overcrowd the pan. Remove the chicken to a plate.
Add shallot, saute for 2 minutes, and add garlic. Saute for 30 seconds more. Add more olive oil if needed.
Pour in chicken stock and deglaze the pan. Allow the mixture to simmer and to reduce in size by half. Once ready, stir in lemon zest and juice. Add remaining butter (2 tablespoon of cold butter), and capers, return the chicken and coat it a couple of times, and serve with fresh parsley.
