Heat 2 tablespoons butter and 2 tablespoons olive oil in a large, nonstick skillet over medium heat.
Stir flour, salt, and pepper together in a shallow dish. Dredge each chicken cutlet in flour mixture and add to the hot pan. Cook chicken, about 3 minutes each side until browned and fully cooked. Remove chicken from pan and set aside.
In the hot pan, whisk in remaining butter, lemon juice, chicken stock, and white wine to create the sauce. Add in capers, parsley, and chicken pieces.
Serve warm with lemon slices or wedges.
Notes
LOWER CARB OPTION: Simply brown your chicken without coating it in flour.