Place a piece of plastic wrap on a thick cutting board.
Place 1 or 2 chicken breasts on wrap. Fold over plastic wrap to cover or cover with another piece.
Use a mallet to beat and flatten the chicken to about 1/4-inch thick.
Remove wrap and place breasts on a plate. Sprinkle each with salt and pepper.
Repeat with remaining chicken breasts. Set aside.
Prepare a large bowl of ice water. Set aside.
Fill a medium cooking pot about halfway with water.
Place pot over medium high heat and bring to a boil.
Add a little salt, to taste, to the water.
Remove the woody ends of the asparagus.
Add asparagus. Boil for 3 - 5 minutes, depending on the thickness of your asparagus spears.
Remove asparagus from pot and drop in bowl of ice water to halt the cooking. The asparagus should be slightly tender when done, not mushy.
Place 1 tablespoon olive oil in a large skillet.
Place skillet over medium heat.
When oil is hot and shimmering, place chicken breasts, one or two at a time, in oil and sauté for 4 - 6 minutes per side, or until the chicken has browned just a bit.
Remove chicken fillets from the pan. Wrap together in foil to keep the fillets warm while you make the sauce.
Repeat with remaining chicken breasts.
Don't clean the pan.
Add two tablespoons oil to the skillet.
When oil is hot and shimmering, add onion and garlic. Sauté for 4 - 5 until onion is soft and fragrant.
Add sliced mushrooms. Sauté for about 2 minutes until mushrooms are just getting soft.
Add Madeira wine, beef stock, 1 tablespoon Worcestershire sauce, Dijon mustard and honey, butter and pepper. Increase heat and bring sauce to a boil. Then reduce heat. Simmer for about 20 minutes or until sauce has reduced to about 1/4 of its original volume, thickened and turned a dark brown color. Remove from heat but keep warm. Rewarm, before using if you make sauce in advance.
Set oven to broil.
Arranging the cooked chicken fillets on a baking pan.
Cross two asparagus spears over each fillet.
Cover each with a slice of mozzarella cheese.
Place pan in heated oven and broil for 3 to 4 minutes or until light brown spots begin to appear on the cheese.
Remove from oven.
Arrange two chicken breasts on each plate.
Spoon 3 or 4 tablespoon prepared Madeira sauce over the chicken.
Serve hot with mashed potatoes.