Preheat a skillet or griddle over medium heat.
In a small bowl, mix together the mayonnaise and Dijon mustard until well combined.
Spread the mayonnaise mixture evenly on one side of each slice of sourdough bread.
On the unspread side of four slices, layer the turkey, bacon, and cheddar cheese. Season with black pepper.
Top with the remaining slices of bread, mayonnaise side up, to form sandwiches.
Spread softened butter on the outside of each sandwich.
Place the sandwiches in the preheated skillet and cook for about 4-5 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove the sandwiches from the skillet and let them cool for a minute before slicing in half.
If desired, add lettuce and tomato slices before serving.