Preheat the oven to 375°F (190°C). Lightly grease a 9×13-inch baking dish with cooking spray or a little olive oil.
Heat a large skillet over medium-high heat. Melt 1/2 tablespoon of the butter with 1/2 tablespoon of the olive oil.
Add the sliced mushrooms and onion. Season with salt and black pepper and cook for about 5 minutes, stirring occasionally, until softened.
Add the minced garlic and cook for about 20 seconds, just until fragrant.
Transfer half of the mushroom mixture to the prepared baking dish and spread it into an even layer.
Return the skillet to the stovetop. Add the remaining butter and olive oil.
Season the chicken breasts with salt, pepper, garlic powder, paprika, and Italian seasoning.
Add the chicken to the hot skillet. Work in batches if necessary, and cook for about 2 minutes per side, until lightly browned.
Arrange the browned chicken over the mushrooms in the baking dish.
Return the skillet to the heat and pour in the chicken broth. Scrape the browned bits from the bottom of the skillet and bring the liquid to a boil. Cook for 4–5 minutes, until slightly reduced.
Spoon the remaining mushroom and onion mixture over the chicken. Sprinkle the mozzarella evenly over the top.
Pour the reduced broth around and over the chicken.
Bake uncovered for about 15 minutes, or until the chicken reaches a safe internal temperature of 165°F (74°C).
Remove from the oven, garnish with fresh parsley, and let the chicken rest for a few minutes before serving.