Place a rack in a large slow cooker. Or make a rack using rings of wadded tin foil.
In a small saucepan, combine the sugar and the water. Cook over medium heat, swirling the pan occasionally, until the sugar is dissolved about 5 minutes. Simmer the mixture without stirring until it begins to turn brown around the edges, about 10 minutes. Gently swirl the pan until the syrup is evenly caramelized.
Protect your hand with an oven mitt. Pour the hot syrup into a 6-cup soufflé dish, turning the dish to coat the bottom evenly. Let cool until the caramel is just set.
In a bowl, whisk together the evaporated and sweetened condensed milks. Beat in the eggs and vanilla until blended. Pour the mixture into the prepared baking dish.
Place the dish on the rack in a large slow cooker. Pour hot water to a depth of 1 inch of around the soufflé dish. Cover and cook on high for 2 to 2-1/2 hours minutes or until a knife inserted near the center comes out clean.
Protecting your hands with oven mitts, carefully remove the dish from the slow cooker. Let cool slightly, then cover and refrigerate until chilled, several hours or overnight.
To serve, run a knife around the inside of the dish. Invert a serving plate on top of the dish and quickly invert the two. Carefully remove the dish allowing the caramel to drizzle over the cream. Cut into wedges to serve.