Heat the oil and butter in a large, heavy-based frying pan and cook the chicken, turning once, over a high heat for 15 minutes or until golden and cooked through. Use a fish slice to remove the chicken from the pan and keep it warm.
Add the crème fraîche to the pan with the mustards and stir for 2–3 minutes until warm but not boiled. Stir in the chopped parsley and season generously with pepper. Serve the chicken on warmed serving plates and spoon the sauce over. Serve with green beans and buttered new potatoes, if liked.