Spread the butter on one side of each of the slices of bread. Top half of the slices of buttered bread with 2 slices of mozzarella cheese.
Close the sandwich so the buttered sides hold the mozzarella in place. Press down gently to adhere the cheese to the bread then carefully trim the crusts off the bread.
In a bowl, beat the eggs until combined. Season with salt and pepper and set aside. In another medium shallow bowl stir together the panko breadcrumbs, Pecorino Romano, lemon zest and garlic powder.
Heat a pan over med heat, add enough oil to reach ¼” up the sides of the pan and heat. Working one at a time, add the sandwich to the beaten egg mixture, coating it on both sides.
Add the sandwich to the panko mixture and gently press to coat the sandwich. Add the sandwich to the hot oil and fry, until golden brown and crispy, about 1 to 2 minutes.
Use a spatula to flip the sandwich cooking until golden brown, about an additional minute. Turn the heat down to medium-low if the outside browns too quickly. The inside should be melty.
Remove to a cooling rack set over paper towels and repeat with the remaining sandwiches until all are cooked. To serve, cut in half diagonally and top with parsley with marinara for dipping.