Slather one side of each piece of bread with mayonnaise. Set plain side up (slathered side down).
Assemble sandwiches with a piece of cheese, dollop of jam, slices of pear, bacon and another piece of cheese and top piece of bread, mayo side facing out. The cheese slices should be touching the bread on both sides.
Heat a griddle or skillet to medium heat (325°F for griddle) and add the sandwiches, pressing down to get maximum surface space in contact with the pan and cheese to melt and stick. Cook for 1-2 minutes or until bread it lightly browned. Flip and repeat on the other side.
Remove to a cutting board and cut in half with one smooth hack. Serve hot!
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