Prepare the bread: Lay the sourdough slices flat and spread a thin layer of Dijon mustard on the inside of two slices.
Assemble the sandwich: Place a slice of cheddar cheese on each piece of bread. On the bottom half, layer the sliced turkey breast, cooked bacon strips, and cracked black pepper. Close the sandwich.
Coat the outside: Mix the softened butter and mayonnaise together in a small bowl. Spread this mixture evenly on the outside surfaces of the assembled sandwiches.
Cook: Heat a skillet over medium-low heat. Add the sandwiches and cook for 4 to 5 minutes per side, covering briefly with a lid to encourage melting, until the bread is golden brown and the cheese is completely melted.