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Preheat oven to 350 degrees F.
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Prepare the caramelized sugar by putting the sugar into a heavy saucepan heated over medium-low heat. Stir. Once the sugar begins to dissolve, DO NOT stir it any further. To do so will ruin your caramel. Instead, tilt the saucepan to move the sugar syrup around in the pan as you watch the sugar change to a dark amber color. You can use a brush dipped into water to brush around the sides of the saucepan to dissolve any sugar crystals that begin to form while your caramel is cooking. It will take from 10-15 minutes for the sugar to caramelize. Be sure to watch the sugar carefully and constantly during this process. You can burn the sugar in an instant. When the sugar is an amber color, take the saucepan off the heat and pour it into the un-greased pan or dish in which you plan to bake your flan. (I used a glass loaf pan.) As you pour the caramelized sugar into the pan, tilt the plan to distribute the caramelized sugar over the bottom of the dish. Let the sugar mixture sit for about 10 minutes.
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Meanwhile, mix your cream cheese until it is smooth. I used my stand mixer. Then, add the eggs one at a time--beating after each addition. Add the sweetened condensed milk, the evaporated milk, and the vanilla to the mixture and mix thoroughly. Pour this mixture over the caramelized sugar in the pan you have prepared.
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Set this pan inside a larger baking dish. (I used a large glass lasagna pan.) Boil some water and pour it into the larger pan until it reaches a depth of about 1 inch.
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Bake your flan in the water bath at 350 degrees F. for 50-60 minutes. Your flan is done when the mixture is set (the center of the flan should jiggle).
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Remove the flan from the larger pan and cool on a wire rack for about an hour. Refrigerate overnight.
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When you are ready to serve the flan, remove it from the refrigerator and run a knife around the edges of the flan. Cover the flan with a large plate. Invert the flan over the dish. Enjoy. Be sure to spoon a lot of the amber sugar sauce over each person's portion of flan.