Pesto Chicken Lasagna

Ingredients

• 1¼ cup whole milk
• 1 large egg, lightly beaten
• 1 pound mozzarella, grated
• kosher salt and ground black pepper to taste
• 2 tablespoons unsalted butter
• 1 tablespoon olive oil
• 4 teaspoons flour
• ½ cup + 2 tablespoons freshly grated Parmesan, divided
• 15 ounces ricotta
• 2 split bone-in chicken breasts, about 1.5 pounds
• 2 tablespoons dried parsley
• 1¼ cup pesto
• 9 lasagna noodles, cooked according to package directions