Heat balsamic vinegar and honey. Pour over figs and infuse for 5 minutes.
Place figs and liquid with red bell pepper in a food processor. Process until smooth. Season to taste, processing again with salt and black pepper (or chile flakes if you prefer a spicy jam). Set aside.
Make Grilled Cheese
Spread a thin coat of mayonnaise evenly on one side of a bread slice. Place it on a plate, mayonnaise side up. Repeat with the other bread slice, placing mayonnaise side down.
On bread slice facing you, spread on 1/4 cup balsamic fig jam. Tile cheese slices on top.
Preheat a skillet on medium for 1 minute. Pickup bread stack, removing the slice from the bottom, bringing it to the top to cover the cheese, mayonnaised sides facing out.
Place sandwich in skillet for 1 1/2 minutes. Carefully flip with a spatula and turn down heat to medium low, cooking other side until golden, about 2 minutes. Slice and serve.