Using a very sharp knife, slice the lemon thinly, and remove any seeds.
Combine the feta, lemon zest, and basil in a small bowl, and mix together.
In a separate, small bowl, combine the butter and Parmesan cheese to form a spread.
You will be making four sandwiches. Brush the Parmesan mixture on one side of each of the pieces of bread. This will be the outside – the side that is cooked against the skillet.
Assemble the sandwiches in layers – first, a layer of mozzarella (using half,) then the lemon slices, third, the feta herb mixture, then the last half of the mozzarella, before topping it with the second slice of bread.
Heat a large skillet to a medium high temperature. Grill the sandwiches on one side until the Parmesan is browned, and the cheese melting, then flip over to brown the other side.