Preheat the oven to 375°F (190°C).
Season both sides of the 4 thinly sliced chicken breasts with salt, pepper, and 1 tablespoon Italian seasoning.
In a large skillet over medium-high heat, melt 2 tablespoons unsalted butter. Add the chicken and brown 2–3 minutes per side until golden (it will finish cooking in the oven). Transfer the chicken to a 13 x 9 x 2-inch baking dish.
Return the skillet to medium heat and add 8 ounces sliced mushrooms. Cook until they begin to soften, about 3–4 minutes.
Pour in 1/2 cup chicken broth and simmer briefly until the mushrooms are tender and the liquid reduces slightly, about 2–3 minutes. Pour the mushroom mixture evenly over the chicken in the baking dish.
Bake uncovered for 15 minutes.
Remove from the oven, sprinkle 1/2 cup shredded mozzarella cheese over the chicken, and return to the oven for 5 more minutes or until the cheese is melted and the chicken is cooked through (internal temperature 165°F / 74°C).
Garnish with chopped fresh parsley and serve.
