Preheat your oven to 375°F (190°C).
Season the chicken breasts with salt and pepper. In an oven-safe skillet, heat olive oil over medium-high heat. Sear the chicken for 3–4 minutes per side until golden. Remove and set aside.
In the same skillet, melt the butter and sauté the mushrooms until soft and browned, about 5–6 minutes. Add garlic and cook for 1 minute until fragrant.
Pour in the chicken broth and heavy cream. Stir in Italian seasoning, bring to a simmer, and let it cook for 2–3 minutes. Stir in half of the mozzarella and all of the parmesan cheese until melted into the sauce.
Return the seared chicken breasts to the skillet. Spoon the sauce and mushrooms over the chicken, then top with remaining mozzarella cheese. Transfer the skillet to the oven and bake for 20–25 minutes, until the chicken is cooked through and the cheese is golden and bubbly.
Let cool slightly. Garnish with chopped parsley and serve hot with mashed potatoes, rice, or crusty bread.