On a cutting board, place 4 slices of bread. To the bread, layer cheese, dressing, cranberry sauce, turkey, mashed potatoes, another layer of dressing and another layer of cheese. Top with remaining bread.
Turn on a panini press, or heat oil in a grill pan, or large skillet over medium-high heat.
Butter the top slice of bread for each sandwich. Carefully tranfer the sandwich to the panini press, grill pan, or hot skillet, butter-side down.
If desired, add a heavy skillet onto the sandwiches. Cook for 2 to 3 minutes. Check the underside of the sandwich. If brown, add butter to the top layer of bread, then carefully flip. If not browned, let cook for another minute or so, until browned. Then flip. (No need to do this step if using a panini press).
Remove from skillet, slice, and serve with warmed gravy at once.