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1
Preheat the oven to 350 degress.
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2
Add the cake mix to the mixing bowl of a standing mixer. (Or a large bowl, if you are going to mix it by hand with a whisk). Add 2 eggs plus 3 yolks (reserve the egg whites for the meringue topping) and 1/2 cup milk or buttermilk. Mix on low speed for 30 seconds or until well blended.
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3
Add the softened cream cheese, sour cream, melted butter, butter rum flavoring, 1 teaspoon vanilla and 2 tablespoons rum (optional) and mix on medium speed for 1 - 2 minutes, until well-blended.
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4
Spread batter into a 9 x 13 inch cake pan. Bake for 20 to 25 minutes, just until a toothpick inserted into the middle comes out clean.
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5
While the cake is baking, make the milk 'syrup' that will soak into the cooled cake: In a bowl, whisk together the condensed milk, the evaporated milk, and the whipping cream (the three kinds of milk, or 'res leches), 1 teaspoon vanilla, a pinch of salt, and 1 tablespoon rum (optional).
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6
Once the cake is out of the oven, use a fork or small skewer to gently poke holes in the cake, Slowly pour the milk mixture over the entire cake. The milk mixture will not soak in immediately, and may pool in the sides and the bottom at first, but it will eventually soak into the cake completely. Tilt pan around some to help distribute the liquid.
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7
Cover the cake with saran wrap and chill for 3-4 hours or overnight.
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8
To make the meringue topping, place the egg whites in the (very clean) bowl of an electric mixer, and attach the wire whisk.
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9
Place the sugar, 1/3 cup water, corn syrup, and pinch of salt in a small saucepan, and bring to a boil.
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10
When the temperature of the sugar syrup reaches about 238 degrees Fahrenheit (after about 3 minutes), turn on the mixer and start beating the egg whites. When the temperature reaches 242 degrees Fahrenheit (117 degrees Celsius), remove the syrup from the heat. (The total cooking time is about 4 minutes, and the sugar syrup should make thin threads if you drizzle it off of a fork, and will have thickened.).
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11
The egg whites should be forming medium stiff peaks. Slowly and carefully pour the syrup down the side of the mixer bowl, into the beaten egg whites. Continue to beat the meringue for 1-2 minutes longer. Stir in 1 teaspoon vanilla and 1 teaspoon rum if desired.
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12
Spread the meringue over cake, and use the back of a spoon to make decorative peaks. Sprinkle cake with powdered cinnamon.
