1. Preheat the oven to 375 degrees F. Butter a 7- by 9-inch baking dish.
2. Arrange the plantains in the baking dish. Combine the brown sugar, granulated sugar and ground cinnamon in a small bowl and sprinkle evenly over the plantains. Sprinkle with the Madeira and top with the butter chunks and cinnamon sticks.
3. Bake until the plantains are very soft and the sugars are caramelized and brown, 50 minutes to 1 hour. Serve warm.
Put yellow and black-spotted plantains in a paper bag. In a couple of days they should be completely black on the outside and perfectly ripe on the inside, exactly how they are needed for this dish.