Mix the sugar and cinnamon in a small bowl, if desired. Melt the butter on a heavy griddle over medium heat. Coat both sides of the bread slices with the melted butter on the grill and arrange on grill. Sprinkle with sugar. Once bread has nice grill marks, about 2 minutes, flip over and grill the sugared side for 2 minutes until caramelized. Transfer the toasts to a plate, sugar side up. Cool slightly, then cut diagonally in half. Eat toasts sugared side down.