Preheat oven to 375°F (190°C).
Season chicken breasts with salt and black pepper.
Set up a breading station with flour, beaten eggs, and a mixture of Panko breadcrumbs and 0.5 cup grated Pecorino Romano cheese, plus 1 tbsp lemon zest.
Dredge each chicken breast in flour, shaking off excess. Dip in beaten eggs, then press into the Panko-Pecorino mixture to evenly coat.
Heat olive oil and 1 tbsp butter in a large oven-safe skillet over medium-high heat. Add the chicken breasts and cook for 2-3 minutes per side until golden browned. Transfer to the oven and bake for 10-12 minutes or until cooked through.
While the chicken is baking, prepare the sauce: In the same skillet on medium heat, melt the remaining 1 tbsp butter. Add garlic and sauté for 1 minute until fragrant. Add 0.25 cup Pecorino Romano, 1 tsp lemon zest, and lemon juice. Stir in heavy cream and chicken broth. Bring to a gentle simmer and cook until thickened slightly, about 3-4 minutes. Season with salt and pepper.
Once the chicken is done, place on serving plates and spoon the warm Pecorino sauce over each piece. Garnish with fresh parsley before serving.