Position the oven rack in the center of the oven, and preheat to 325 degrees F. Set six 9-ounce soufflé dishes in a roasting pan. Combine 1 cup of sugar and the water in a heavy small saucepan. Stir over medium-high heat until the sugar dissolves. Boil without stirring until the syrup turns a deep golden brown color, occasionally brushing down the sides of the pan with a wet pastry brush and swirling the pan, about 4 minutes. Immediately pour the caramel into the soufflé dishes, dividing equally. Set aside.
Meanwhile, pour the milk into a heavy medium saucepan. Scrape in the seeds from the vanilla bean; add the bean. Bring to a simmer over medium heat. Remove from the heat.
Whisk the remaining 1 cup of sugar and the eggs in a large bowl until the sugar is dissolved and the mixture is foamy, about 5 minutes. Gradually whisk in the hot milk mixture. Remove the bean. Pour the custard into the prepared soufflé dishes, dividing evenly. Transfer the roasting pan to the oven. Pour enough hot water into the pan to come halfway up sides of the dishes.
Bake until the outer 1-inch perimeters of the flans are softly set but the centers are still loose, about 35 minutes (the custard will firm up after it is refrigerated). Transfer the flans to a rack and cool. Refrigerate until cold, about 2 hours. Cover and refrigerate overnight.
DO AHEAD: The flans can be prepared up to 1 day ahead. Keep refrigerated.
Run a small sharp knife around each flan to loosen them from the dish. Working with one flan at a time, place a plate atop the flan; invert the flan onto the plate. Shake gently to release the flan from the dish (you will hear it being released). Carefully remove the dish, allowing the caramel syrup to run over the flan.