In a medium saucepan, heat the cream, milk, cinnamon stick, and ½ cup (100g) of the sugar over medium-high heat, stirring to dissolve the sugar, until steaming. Let cool to room temperature. Cut the bread into 2-x-2-x-4-inches (5-x-5-x-10-cm) rectangular bars. Place them in a shallow dish that will accommodate them in a single layer, pour the milk mixture over, and let soak for 10 minutes. Flip them over as needed to ensure even soaking.
In a large skillet, melt 2 tablespoons of the butter with 2 tablespoons of the sugar over medium-high heat. Remove 2 pieces of bread from the milk mixture and set them on a paper towel to blot excess liquid. Once the butter and sugar have melted, add the 2 pieces of bread to the pan. Cook for 1 minute before flipping 90º. Cook for another minute, then flip 90º again. The sugar and butter should be starting to caramelize. Flip again and, after another minute, flip to the last side and cook for 30 seconds.
Finally, swirl the pan to distribute the caramelized sugar-butter mixture and flip the bread pieces once more, with the most presentable side down. Cook for 1 minute. Gently remove the bread pieces, with their most presentable side up, to a sheet pan. Wipe out the skillet with paper towels, then cook the remaining bread in batches of two, using 2 tablespoons of the remaining butter and 2 tablespoons of the remaining sugar for each batch. Serve warm*.
*For an extra-special touch, sprinkle the top of each warm bread piece with additional sugar, then melt the sugar under a broiler or with a kitchen torch until it bubbles, as for crème brûlée. Let the caramelized sugar cool for a couple of minutes to a crunchy coating (and to avoid burning your tongue!).