Remove the Mozzarella from the packets and drain them of liquid. Slice into 1cm thick slices and place on a plate with a piece of kitchen paper underneath.
Lay the pieces of bread on a chopping board. Place 1tsp of Pesto each on 3 slices on bread and spread to the edge with a knife, leaving a 1cm gap. Divide the slices of mozzarella and place on top of the pesto, again leaving a gap. Season with a little salt and a generous amount of pepper.
Use a brush or your finger and wet the edges of the sandwich with the beaten egg, then place a piece of bread on top and press down firmly around the edges to seal. Repeat so you have 3 sandwiches.
Place a large frying pan on a medium to high heat and add half the Olive Oil. When hot, add the sandwiches. The Olive Oil should be hot enough so that they fry and being to crisp. Cook for 3-4 minutes or until golden, turning the heat down if necessary. Remove the sandwiches from the pan, add the remaining Olive Oil and when hot again, place the sandwiches back in, uncooked side down. Cook again for 3-4 minutes. Press the sandwiches in the middle – if they feel soft and giving, then they are ready. If they feel a bit firm, cook for a further 2 minutes on each side.
Cut in half and eat immediately, be aware though that the contents can be very hot and will ooze out.