Preheat the oven to 375°F (190°C).
Pat 4 thinly sliced chicken breasts dry, then season both sides with salt and pepper to taste and sprinkle evenly with 1 tablespoon Italian seasoning.
In a large skillet over medium-high heat, melt 2 tablespoons unsalted butter. Add the chicken breasts and cook until browned on both sides (about 2–4 minutes per side); the chicken does not need to be fully cooked through. Transfer the browned chicken to a 13 x 9 x 2-inch baking dish.
In the same skillet, add 8 ounces sliced mushrooms and ½ cup chicken broth. Bring to a simmer and cook until the mushrooms are tender and the liquid has reduced slightly, about 3–5 minutes.
Pour the mushroom and broth mixture evenly over the chicken in the baking dish.
Bake uncovered at 375°F for 15 minutes.
Remove the dish from the oven, sprinkle ½ cup shredded mozzarella cheese evenly over the chicken, then return to the oven and bake an additional 5 minutes, or until the cheese is melted and the chicken is cooked through (internal temperature 165°F).
Garnish with fresh chopped parsley and serve.