First, mix the mozzarella cheese and pesto (leave 1 tablespoon aside for the bread) together in a bowl to combine.
Next, place mayo on one side of all the slices of bread and pesto on the other sides of the slices of bread (the mayo side will be the outside of sandwich and pesto side will be the inside of the sandwich).
Now, add 1/2 cheese pesto mixture to bread and close the sandwich (mayo slices outside). Repeat for the other sandwich.
Next, cook in a pan on medium heat for 2 minutes per side.