Pre heat oven to 350°. Generously spray a 9 by 13 dish.
In a large bowl, whisk together flour, sugar, salt, and powder to sift. Set aside.
In a small bowl, mix together coconut milk, vanilla, cream of coconut, lime juice, and oil. set aside.
In a separate clean bowl, add egg whites. beat with a hand mixer until stiff peaks form. About 5 or so minutes. You should be able to turn your bowl upside down without spilling. (be careful with that test ;))
Add ½ of wet mixture to dry mixture, fold. Add other ½ of wet to the dry and mix until all combined. Once combined, gently fold in ⅓ of egg whites to batter, once mixed, add in the rest of the egg whites and carefully fold until no white streaks are left. BE GENTLE!!! This step is what makes the cake so soft and fluffy.
Pour batter in prepared dish, bake for 35 minutes, or until top is golden brown and a toothpick comes out clean.
Let cake cool for 5 minutes before glazing.