Preheat oven to 350 degrees F. Spray a 9x13-inch baking pan with cooking spray (or rub with butter) and line with a sheet of parchment. Set aside.
In a medium bowl, add the all-purpose flour, baking powder and salt. Whisk until combined.
To the bowl of a stand-up mixer with the paddle attachment (or you can use a large bowl with an electric mixer), add the butter and sugar. Beat until light and fluffy, about 2 to 3 minutes. In a measuring cup, pour in the milk, egg whites, cream of coconut and coconut extract; whisk until combined.
Turn the mixer to low speed and, alternating between the dry ingredients and the liquid ingredients (the egg white mixture), add to the butter/sugar mixture until the batter is relatively smooth.
Pour the batter into the prepared baking pan and transfer to the oven to bake for 22 to 25 minutes, until a skewer inserted into the center comes out clean.
Allow the cake to cool in the pan for about 5 minutes. And then brush with the rum syrup. I like to do it when it's warm so the cake absorbs the rum syrup. Allow to cool in the pan and then transfer to any serving tray you like.