Step 1

Sprinkle both sides of chicken fillets with salt and pepper. Place 1/3 cup all-purpose flour in a plate and dredge fillets in flour to coat both sides. Shake off excess flour.

Step 2

Heat oil in a frying pan. Brown chicken on both sides. Transfer fillets to oiled 13x9-inch baking dish.

Step 3

To make sauce, melt butter in same pan. Add mushrooms and cook until golden brown.

Step 4

Sprinkle mushrooms with 3 Tbsp flour and let cook, stirring, for 1-2 minutes. Slowly stir in chicken broth, wine and milk. Cook, stirring often, until it begins to thicken and becomes bubbly. Season to taste with salt, pepper and thyme.

Step 5

Pour mushroom sauce over chicken. Top each fillet with one slice cheese. Cover dish with aluminum foil and bake for 30 minutes in preheated 350 F (175 C).

Step 6

Remove foil and broil for 1 to 2 minutes to brown the cheese. Serve sprinkled with chopped parsley.