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 four slices, 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.
Spread 1 tablespoon of softened butter on the top of each sandwich.
Place the sandwiches in the preheated skillet, buttered side down. Cook for about 4-5 minutes until golden brown.
Carefully flip the sandwiches, adding the remaining butter to the skillet if necessary. Cook for another 4-5 minutes until the cheese is melted and the bread is golden brown.
Remove from the skillet, slice in half, and serve warm.