Preheat a skillet or griddle over medium heat.
In a small bowl, mix together the mayonnaise and Dijon mustard. Spread this mixture evenly on one side of each slice of sourdough bread.
On the unspread side of 4 slices of bread, layer the turkey, cheddar cheese, and crumbled bacon. Season with salt and pepper to taste.
Top with the remaining slices of bread, spread side up, to create sandwiches.
Spread softened butter on the outside of each sandwich.
Place the sandwiches in the preheated skillet or griddle. Cook for about 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from heat, slice in half, and serve warm.