Pour 2 cups of sugar into the center of a deep saucepan. Carefully pour the water around the sugar, trying not to splash any sugar onto the sides of the pan. Do not stir; gently draw your finger through the center of the sugar twice, making a cross, to moisten it. Over medium-high heat, bring to a boil without stirring. Reduce the heat to a fast simmer and cook without stirring until amber-caramel in color, 10 to 20 minutes. Immediately remove from the heat. Meanwhile, set 6 (8-ounce) ramekins or shallow coffee cups nearby. When the caramel is cooked, quickly pour about cup caramel into each ramekin and swirl to coat the sides. Set aside in a large roasting pan to cool. Bring a medium sized, full pot of water to a boil. Preheat the oven to 300 degrees. In a saucepan, bring the milk, vanilla bean and cinnamon stick to a boil over medium heat. Immediately turn off the heat and set aside to infuse 10 minutes. Add the chopped chocolate and whisk to melt and combine. Meanwhile, in a large bowl, whisk together the eggs, additional egg yolks, and the remaining 1-cup sugar. Whisk about 1/2 cup of the hot milk into the egg mixture. Whisk the remaining hot milk into the egg mixture. Strain the mixture into a pitcher to smooth it and to remove the vanilla bean and cinnamon sticks. Pour the mixture into the caramel-lined ramekins. Place the roasting pan onto the rack in the oven. Pour the boiling water into the roasting pan, but not into the custard cups, up to the same level as the custard in the cups. Bake in the center of the oven until set in the center, 30 to 35 minutes. Remove the cups from the water bath and let cool. Tightly cover each ramekin with plastic wrap. Refrigerate at least 2 hours. (Or refrigerate until ready to serve, up to 24 hours.) To serve, turn flans out onto plates (you may need to dip the bottom of each ramekin in hot water to loosen the caramel, and/or run a knife around the edge of the ramekin). The caramel will pour out and serve as the sauce.