Skillet Gratinate of Chicken and Mushrooms - Lidia

Ingredients

• 4 tablespoons unsalted butter
• 1 tablespoon extra-virgin olive oil
• 8 shiitake mushrooms, stems removed
• All-purpose flour, for dredging
• 2 large boneless, skinless chicken breasts, halved crosswise/butterflied (about 1 1/2 pounds)
• Kosher salt
• Freshly ground black pepper
• 1 firm medium-sized beefsteak tomato (about 1 pound), 4 slices, remainder chopped and reserved for the sauce
• 4 large fresh sage leaves
• 1/2 cup dry white wine
• 1 cup chicken broth, preferably homemade or low-sodium store-bought
• 3/4 cup freshly grated Italian fontina
• 1/4 cup freshly grated Grana Padano or pecorino
• 2 tablespoons chopped fresh Italian parsley