Heat a panini press or cast iron pan to medium-high heat.
For each sandwich, spread butter on one side of two slices of bread, and spread a layer of fig jam on the other side of each slice. To one slice add a layer of sliced cheese, several apple slices, and a layer of more cheese. Top the sandwich with the other slice of bread, buttered side up.
Using panini maker or preheated pan, grill paninis until the cheese is melted and the bread is toasted on both sides, about 4 to 5 minutes.