Heat griddle or large skillet over medium-low heat. Alternatively you can use your panini press if you have one.
Assemble sandwich: Generously spread Dijon on 4 slices of bread. Top with slices of Cheddar, 3 pieces of bacon, apple slices and additional Cheddar. Place the remaining bread on top and spread with butter. Place on skillet buttered-side down and butter the remaining side. Cook until cheese is slightly melted and bread is browned. Flip the sandwich and continue to cook until cheese is thoroughly melted and sandwich is golden brown.