Heat the oil in a skillet over medium high heat.
Season the chicken with salt and pepper to taste, and place into the heated skillet.
Sear the chicken evenly on both sides until browned and cooked partially. Remove and set aside. Drain the oil from the skillet.
Reduce the heat to medium, and add the butter to the skillet.
Place the mushrooms and onions into the skillet, and saute until softened.
Stir in the garlic, and saute another 30 seconds.
Pour in the sherry, and simmer until half of the liquid has been reduced.
Add the chicken broth to the skillet, and return the chicken.
Cover and simmer until the chicken is mostly cooked through.
Stir in the asparagus and Italian seasoning.
Cover and simmer until the asparagus has been cooked.
Stir in the heavy whipping cream and simmer until the sauce thickens slightly.
Remove the skillet from the heat, and sprinkle the mixture with the mozzarella cheese.
Place the lid on the skillet, allow the cheese to melt and then serve.