Bring a pot of salted water to a boil. Boil the asparagus for two minutes, drain and set aside.
In a large skillet, add a large drizzle of olive oil and heat over medium-high heat. Once hot, add in the mushrooms. Sauté for about 2 minutes.
Add the shallots and garlic and sauté for another 4 minutes. Remove from the skillet and set aside.
In the same skillet, add another drizzle of olive oil and the butter. Let it melt over medium/high heat. Place the chicken breasts into the skillet and cook for three minutes on each side.
Lower the heat and slowly pour in the wine. Allow the alcohol to evaporate for about two minutes and then remove the chicken from the skillet, leaving the wine sauce in the pan and set aside.
Add one to two cups of the chicken stock and all of the heavy cream to the skillet. Mix together and bring to a boil. If not enough liquid, add a little more of the chicken stock. You can add more or less depending on how thick you would like the sauce to be. Once boiling, reduce the heat to low and allow to simmer for 6 minutes.
Sprinkle in some parsley and then place the chicken back into the pan. Place the mushrooms evenly over the chicken breasts. Place the asparagus along the sides of the pan.
Sprinkle the mozzarella evenly over top of the pan and then cover with a lid and let simmer over low heat for 15 minutes, until the cheese has melted. **You can also put it into the oven with no lid at 400°F to melt the cheese and thicken the creamy sauce.
Remove from the heat and serve with your favorite side dish. Sprinkle with some parsley and enjoy.