Carefully cut each chicken breast lengthwise into two pieces.
Place the chicken between two pieces of plastic wrap or parchment paper and pound each one with a mallet or meat tenderizer until the pieces are approximately 1/4 inch thick.
Place the flour in a shallow pan. Season the chicken with salt and pepper and then dredge it in the flour to coat well.
In a large sauté pan, heat the vegetable oil over medium high heat.
When the oil is hot, add the chicken and cook until it is fully cooked and golden brown – about 3 to 4 minutes per side.
Remove the chicken to a platter and cover with foil to keep warm.
Wipe the excess oil out of the pan with paper towels.
Reduce the heat to medium and add the butter. When the butter is melted, add the sliced mushrooms and sauté them for 2 to 3 minutes.
Season the mushrooms with salt and pepper, then add the marsala, sherry, cream and chicken stock.
Bring the sauce to a boil and let it reduce for about 3 minutes. Taste and add more salt and pepper if needed.
Pour the mushrooms and sauce over the chicken.
Garnish with chopped parsley and serve.