Prepare the Sandwiches
Working with the bread slices, spread a thin layer of mayonnaise on one side of each slice if using. This optional step adds extra richness to the final dish. Arrange the mozzarella slices evenly between two bread slices to create 2 complete sandwiches, being careful to ensure the cheese doesn't extend beyond the edges of the bread.
Create the Coating Mixture
In a shallow bowl, thoroughly whisk together the eggs and milk, then season with salt and pepper to taste. In a separate shallow bowl, combine the flour with the panko breadcrumbs (if using) and season with additional salt and pepper. Prepare a small tray lined with parchment paper to hold your coated sandwiches.
Coat the Sandwiches
Take each sandwich and dip it completely in the egg-milk mixture, ensuring all surfaces are well coated. Transfer the wet sandwich to the flour mixture, gently pressing to adhere the coating evenly on all sides. Place the coated sandwich on your parchment-lined tray and repeat the process with the second sandwich.
Chill and Heat Oil
Refrigerate the coated sandwiches for 20 minutes to allow the coating to set properly, which prevents it from falling off during the frying process. Meanwhile, heat the oil in a cast iron skillet or heavy pot to approximately 350°F, creating an oil depth of about 1 inch.
Fry the Sandwiches
Using a spatula, carefully lower each chilled sandwich into the hot oil. Fry for approximately 2 minutes until the bottom side turns a beautiful golden brown, then gently flip and fry the other side for an additional 2 minutes. The ideal result features a crispy exterior coating while ensuring the cheese inside melts to perfection.
Rest and Serve
Transfer the fried sandwiches to a cutting board and allow them to cool briefly for about a minute. Using a sharp serrated knife, cut each sandwich with care - first cutting halfway through from one side, then flipping and cutting from the opposite side, stopping before cutting completely through the melted cheese center. This technique preserves the gooey cheese interior. Serve immediately while hot and enjoy the cheesy stretch with each bite.