Combine the shredded cheddar and Gouda in a small bowl.
Spread one side of each slice of bread evenly with softened butter.
Place three slices of bread on a work surface with the buttered sides facing down.
Divide half of the cheese mixture among the bread slices.
Top each with turkey, followed by a thin layer of cranberry sauce. Season the turkey lightly with black pepper, if desired.
Sprinkle the remaining cheese over the cranberry sauce. Top with the remaining bread slices, buttered sides facing out.
Heat a large skillet or griddle over medium-low heat.
Add the sandwiches and cook for about 3 to 4 minutes, until the bottoms are crisp and golden brown.
Carefully flip the sandwiches. Reduce the heat to low if the bread is browning too quickly.
Cook for another 3 to 4 minutes, until the second side is golden and the cheese is completely melted. Cover the skillet for a minute or two if needed to help the cheese melt.
Transfer the sandwiches to a cutting board and let them rest for about 1 minute before slicing.
Serve immediately while the bread is crispy and the cheese is hot and melty.