To make a Mexican three-milk, or tres-leches, cake, preheat the oven to 350 degrees Fahrenheit. Sift together 1 1/2 cups all-purpose flour and 1 teaspoon baking powder. In a separate bowl, beat together 1/2 cup unsalted butter and 1 cup white sugar until light and fluffy. Mix in 5 eggs and 1/2 teaspoon vanilla extract. Add 2 tablespoons of the dry ingredients to the wet ingredients, and mix well to blend them. Repeat until all the dry ingredients are incorporated.
Prepare a 9-by-13-inch baking pan by coating it with unsalted butter and all-purpose flour. Pour the cake batter into the pan, and bake it in the oven for approximately 30 minutes.
Use a fork to poke several holes into the finished cake. Allow the cake to cool. In a mixing bowl, combine 2 cups whole milk, 1 14-ounce can of sweetened condensed milk and 1 12-ounce can of evaporated milk. Pour the three-milk mixture over the top of the cake, and allow it to soak into the fork holes.
Combine 1 1/2 cups heavy whipping cream, 1 cup white sugar and 1 teaspoon vanilla extract. Whip the ingredients until they thicken, and then spread the topping over the cake to serve.