1. Cake: Preheat oven to 350 degrees. Butter and flour a 10-inch springform pan. Whisk together flour, baking powder, baking soda, and salt. In another bowl, stir cream of coconut and vanilla.

2. Beat butter and coconut oil on medium-high until smooth. Slowly add sugar; beat until pale and fluffy, 3 to 5 minutes. Reduce speed to medium; add eggs, 1 at a time, beating well after each and scraping down bowl as needed. With mixer on low, add flour mixture in 3 batches, alternating with 2 batches of cream-of-coconut mixture. Beat until just combined.

3. Topping: Whisk egg whites and salt with a mixer until thick and frothy, about 1 minute. Stir in milk and vanilla. Fold in coconut.

4. Spread batter in pan. Dollop topping over batter; carefully spread in an even layer. Bake on a rimmed baking sheet until a toothpick comes out with just a few moist crumbs, about 1 hour (tent with foil if browning too quickly). Let cool completely; remove from pan. Cut into wedges, drizzle with sauce, and serve with extra sauce on the side.