Spread an even layer of mayo onto each slice of bread. Layer cheese on top and sandwich two sides together, making sure the mayo coated side is on the inside of the sandwich. Slice into quarters.
Crush the crackers into coarse crumbs in a medium sized bowl. Set aside.
Beat together the two eggs and milk.
Dip each quarter of the sandwich into the milk mixture first, then into the breadcrumbs. Repeat until all are coated. Lay the sandwiches on parchment paper and place in the fridge to chill.
While the sandwiches are chilling, heat the oil in a pot (about 2 inches deep) on medium high heat. The ideal temperature is 350F, if the oil isn't warm enough your sandwiches will be soggy.
Once your oil is hot fry the sandwiches till golden brown, drain on a paper towel, and enjoy! Serve warm.