In a saucepan, combine all ingredients and simmer mixture, stirring occasionally until cranberries have bursted and mixture has thickened, about 20 minutes. Transfer to a serving dish, cover, and chill for at least 2 hours.
Spread butter on each slice of bread. On one slice add cheese, turkey, Canadian bacon, thickened cranberry sauce, and more cheese. Top with the other bread slice (there should be cheese next to each bread slice).
Cook in panini maker. If you don't have one, heat a non-stick skillet over medium heat. Put the sandwich in the skillet and place something heavy on top to press it down. Cook until bread is golden and cheese melts.
Slice and serve alongside more cranberry sauce if desired.