In a medium bowl, evenly mix together the shredded turkey and sauce.
Butter each bread slice on one side. Lay 2 slices of bread on your cutting board or counter, butter side down, and divide turkey mixture between them. Divide cheese between the two sandwiches and place on top of the turkey. Top them with the other pieces of bread, the butter side facing up.
Heat a saute, cast iron or grill pan over medium heat. When the pan is hot, add enough sandwiches that can fit into the pan. Press the sandwiches down with a spatula or place a heavy pan on top of them. Cook for a minute or two, until the bread is browned, then flip and repeat the process on the other side. Remove sandwiches from pan when the cheese has melted.
Let cool for a minute before slicing in half; serve warm.