Combine the white sugar with the water in a small, heavy saucepan and bring to a boil. Cook until the sugar reaches a dark golden brown. Immediately pour about 2 tablespoons into each of the ramekins, tilting to spread the caramel evenly along the bottom. Arrange the ramekins in a baking dish 2 inches deep and set aside.
Combine the milk, cream, cinnamon stick and vanilla bean in a heavy saucepan. Bring just to a boil, cover and remove from the heat. Let steep for about 30 minutes.
Preheat oven to 325 degrees. Whisk the eggs, yolks, brown sugar, molasses and Amaretto together in a medium bowl. Uncover the milk mixture and return it to the stove. Bring just to the boil again. Whisk about one-third of the hot milk into the egg-sugar mixture to temper it. Whisk in the remaining hot milk. Strain the custard through a fine sieve. (We skipped this step.) Pour into the caramel-lined ramekins, filling them to just below the rim. Pour enough warm water into the bottom of the baking pan to reach halfway up the sides of the ramekins. Bake for 30 to 40 minutes, or until almost set but still somewhat liquid in the center.
Chill completely before serving. To unmold, run a small knife around the edge of the custard, invert onto a serving plate and give the ramekin a firm, sideways shake.