Butterfly the chicken breasts to get them uniform in size before pounding. To do this, run a sharp knife under the tenderloin side from the inside center, through the thick tenderloin, almost to the edge and then fold it open. Then turn the breast around and do the same by running the knife from the center through the thickest part out almost to the edge and fold that open (picture the wings of a butterfly). Cover with plastic wrap and pound to about ¼ inch thick. Repeat for other breast then cut both breasts in half to yield four pieces. (Any shape is fine).
Mix flour, salt and pepper in a medium bowl. Mix eggs and milk in a second bowl. Place seasoned bread crumbs in a third bowl.
Dredge each piece in the flour, shake off excess and then coat with egg wash. Finally coat with the breadcrumbs and lay out on a plate. Place the plate in the refrigerator while making the sauce.
In a small pan, cook stock and reduce to one cup. Add milk, heat and hold on low.
In a medium skillet over medium heat, melt the 4 tablespoons of butter and add shallots. Cook for two minutes and add mushrooms and thyme. Continue to cook. The mushrooms will give up some liquid then the liquid will evaporate, about five minutes. Add flour and stir and cook for three more minutes.
Add milk and stock mixture to mushroom mixture one third at a time, stirring as you go.
Season with salt, pepper and lemon zest. Reduce flame to low and hold while you cook chicken.
In a large sauté pan over medium to medium high heat, melt 2 tablespoons of butter with the two tablespoons of oil until hot.
Remove chicken from refrigeration and fry pieces in hot fat until browned on both sides. Because they are pounded thin, they will only take but a few minutes on each side.
Remove to paper towels then place on a serving platter and drizzle lemon juice over each piece.
Pour sauce over the cutlets or serve sauce on the side and finish by sprinkling on chopped parsley.
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