Use a sharp knife to slice the side of the chicken breasts, without cutting all the way through. Open the chicken up like a book (this is called butterflying).
Place the chicken breasts between two large pieces of parchment paper and pound as flat as possible with a rolling pin or a bottle. Peel the paper off and season well with salt and pepper on both sides.
Put the flour on a shallow plate and dip the chicken breasts into the flour to lightly coat and set aside. Shake any excess flour off.
Heat two tablespoons and one tablespoon of olive oil in a large frying pan over medium-high heat. Fry the chicken for 2-3 minutes on each side until golden (you may need to do this in batches). Transfer to a plate and set aside.
Wipe the frying pan with some kitchen towel. Heat the remaining butter and oil and sauté the shallots and garlic over low heat for five minutes, stirring so that they don't stick. Add the mushrooms and cool for 2-3 minutes.
Add the wine and turn heat to high. Cook for 10 minutes or until the liquid is reduced by about half.
Reduce the heat and stir in the chicken stock and bring to a simmer. Add the chicken breasts and cook for 10 minutes.
Stir in the cream and simmer for a few minutes over low heat.
Check the seasoning. Serve sprinkled with parsley over mashed potatoes or mashed cauliflower for a low carb option.