Butterfly the chicken and place a piece of plastic wrap over the top of the chicken on the cutting board. Pound flat with a mallet or rolling pin. Sprinkle with salt and pepper on both sides.
Place the flour in a bowl and dredge the chicken through the flour until coated. Shake off any excess.
Add 1 tablespoon each of butter and oil to a saute pan and heat to medium-high. Saute the chicken until browned on both sides; about 5 minutes. Remove to a plate.
Turn the heat down to medium and add the remaining 1 tablespoon butter and oil to the pan. Place the mushrooms cut side down in the pan and cook until browned. Flip the mushrooms over.
Next, add the onions and stir with the mushrooms until both are browned and soft. About 5 minutes.
Pour in the marsala, chicken stock, and heavy cream. Bring to a boil, and place the pieces of chicken on top of the sauce. Simmer on medium-low for 5 minutes.
Sprinkle with parsley, serve, and enjoy.