Preheat oven to 400F, and move the rack to the top third of your oven. Cut the woody ends off the asparagus, then cut the asparagus into thirds. Boil a pot of water. Once the water is boiling, cook the asparagus for 2-3 minutes (it'll be tender-crisp by the time the recipe is done) then rinse under cool water, drain, and set aside.
Meanwhile, cut the chicken breasts in half lengthwise and season with the garlic powder and salt & pepper.
Add the oil and 1 tablespoon of the butter to a skillet over medium-high heat. Once hot, add the chicken and cook it for about 5-6 minutes/side until golden (it'll finish cooking in the oven if it's not quite cooked through). Transfer chicken to a plate.
Add the remaining butter to the skillet, along with the mushrooms and garlic. Sauté for 5 minutes.
Add the Madeira wine and beef broth to the skillet. Scrape any brown bits off the bottom of the pan and let it bubble for 5 minutes.
Make the cornstarch slurry by combining 1 tablespoon of cornstarch with 1 tablespoon of cold water and stirring it together in a small bowl. Pour it into the skillet and let the sauce continue bubbling for another 5 minutes (it should thicken up up a fair bit and will thicken a little more in the oven).
Add the chicken back to the skillet and spoon some mushrooms over top of each piece. Arrange the asparagus around and on top of the chicken and then sprinkle the mozzarella over top (concentrate on the chicken but you can sprinkle it all over the skillet).
Transfer the skillet to the oven and cook for 5-7 minutes or until the cheese has melted and the chicken is cooked through (165F). Broil for a couple of minutes if desired (watch it carefully).
Season with extra salt & pepper as needed and serve immediately.