Place each chicken breast between two sheets of plastic wrap and gently pound them with a meat mallet until they are about 1/2 inch thick. This will help tenderize the chicken and ensure even cooking.

In a shallow dish, combine the flour, garlic powder, paprika, salt, and black pepper. Mix well. Coat each chicken breast with the seasoned flour, shaking off any excess.

In a large skillet, melt the butter with the olive oil over medium heat. Add the coated chicken breasts to the skillet and cook for about 4-5 minutes per side, or until they are golden brown and cooked through. Remove the chicken from the skillet and set aside.

In the same skillet, add the sliced mushrooms and minced garlic. Sauté until the mushrooms are tender and lightly browned. Pour in the chicken broth and white wine, scraping the bottom of the skillet to deglaze it. Let the sauce simmer for about 5 minutes to reduce slightly.

Preheat your oven to 375°F (190°C). Place the sautéed chicken breasts in a baking dish and pour the mushroom sauce over them. Sprinkle the shredded mozzarella and grated Parmesan cheese on top. Bake in the preheated oven for approximately 15 minutes, or until the cheese is melted and bubbly.