Cook the 8 slices bacon in a skillet over medium heat until crisp. Drain on a paper towel.
Make the spread. Stir together the ¼ cup mayonnaise, 2 tablespoons Dijon mustard, and 1 tablespoon honey until smooth.
Spread the honey mustard on one side of each of the 8 bread slices. On 4 of the slices, layer the 1 pound deli turkey, followed by a slice of cheddar, the crisp bacon, thin apple slices, red onion, and a handful of arugula.
Top with the remaining bread slices, spread side down.
For a warm, melty version, spread the outsides of each sandwich with the softened butter and toast in a skillet over medium heat for 2 to 3 minutes per side, until golden and the cheese begins to melt. For a cold sandwich, skip this step.
Slice each sandwich in half and serve.