Preheat oven to 350 degrees. Generously butter a 9-by-13-inch glass baking pan. Whisk together egg whites, baking soda, and salt in a stand mixer fitted with whisk attachment on medium speed, until soft peaks form, 4 to 5 minutes.
Add egg yolks to egg-white mixture, and whisk until completely combined. Gradually add sugar, and whisk until combined. Fold in butter and coconut with a rubber spatula.
Sift 1/4 cup flour onto mixture; fold to combine. Repeat with remaining flour, folding in 1/4 cup at a time. Pour batter into pan; bake until golden and a toothpick inserted into the center comes out clean, 20 to 25 minutes.
Meanwhile, whisk together 1 cup heavy cream, the coconut milk, and condensed milk. As soon as cake is removed from oven, pour cream mixture over cake. Let cake cool completely in pan on a wire rack. Cover cake with plastic wrap, and refrigerator at least 5 hours and up to 8 hours.
Just before serving, whisk remaining cup heavy cream until soft peaks form, and spread over cake. Serve with mixed berries.