Preheat the oven to low to keep the chicken warm later. Heat the oil and butter in a frying pan until sizzling. Meanwhile, season the chicken breasts with black pepper.
Add the chicken to the pan and cook for 2–3 minutes on each side until golden, then reduce the heat to low, cover and continue cooking for 8–10 minutes, turning once.
While the chicken is cooking, trim and slice the spring onions. Peel and finely chop the garlic. Clean and slice the mushrooms.
When the juices of the chicken run clear, transfer the breasts to a plate, cover and keep warm.
Add the spring onions, garlic and button mushrooms to the pan and fry over moderate heat for 3–4 minutes, or until softened.
Meanwhile, chop enough parsley to give 2 tablespoons, and enough thyme to give 2 teaspoons.
Stir the flour into the pan and cook for 1 minute, then add the stock and bring to the boil, stirring constantly. Cook the mushroom sauce for 2–3 minutes, then reduce the heat, add the cream, parsley, thyme and mustard and stir well. Return the chicken breasts, and any juices, to the pan and heat gently for 2–3 minutes more.
Put the cooked chicken breasts onto warmed plates and spoon over the mushroom sauce.