Set a rack in the center of the oven, and preheat to 325°F. Place a 10-inch pie plate by the stove. In a small, heavy pot over medium-high heat, add ½ cup plus 3 tablespoons (5¼ ounces) sugar, ¼ teaspoon salt, and ⅓ cup cold water. Stir with a spoon until the sugar has dissolved, then cook until the syrup becomes a deep copper color and registers 240°F on a candy thermometer, about 10 minutes.
Immediately pour the hot caramel into the pie plate, and swirl the plate gently until the caramel coats the bottom in an even layer. Set aside.
In a small pot over medium-low heat, add the milk, cream, chiles, and cinnamon. Bring to a bare simmer, then turn off the heat, cover the pot, and set aside to steep for 15 minutes.
Meanwhile, in a medium pot, add enough water to reach an inch or two up the sides. Set a large bowl on top, (The bottom of the bowl should not touch the water.) Add the chocolate to the bowl, and bring the water to a simmer. Let cook, stirring the chocolate occasionally with a rubber spatula until completely melted, then remove the bowl. Pour the warm milk mixture into the chocolate, and whisk to combine.
In a large bowl, whisk the remaining ½ cup plus 3 tablespoons sugar with the eggs, egg yolk, vanilla, and the remaining ¼ teaspoon salt. Add the chocolate mixture, and whisk to combine.
Set a fine strainer over a large bowl, and strain the chocolate mixture, pressing on the solids with a spatula or the back of a spoon to extract as much liquid as possible. Discard the solids, and pour the liquid into the pie plate.
Bring a kettle of water to a boil. Place the pie plate in a large roasting pan, and place the pan in the oven. Carefully add enough boiling water to the roasting pan to reach halfway up the sides of the pie plate. Cover the pan tightly with aluminum foil, and bake until the custard is set but still jiggly, about 1 hour 10 minutes.
Remove the pan from the oven, remove the pie plate, and let cool on a wire rack for 30 minutes. Refrigerate until completely chilled, about 4 hours. To remove and serve, run a thin knife along the sides of the pie plate to help release the flan. Overturn a large, flat serving dish atop the pie plate. Holding them together firmly, flip the pie plate over to release the flan. Slice into wedges and serve.