Preheat the oven to 350 degrees F. Grease a 9x13 inch baking pan.
Whisk together the cake flour, baking powder and salt. Set aside.
Combine the coconut milk, regular milk and vanilla in a liquid measuring cup. Set aside.
With the electric mixer, preferably a stand mixer with paddle, beat the butter and sugar until light and fluffy.
With the mixer on low (or by hand and using a big spoon or scraper), add the flour mixture and the milk mixture to the creamed mixture alternately. Stir until blended.
If using a stand mixer, switch to a new bowl and attach the whisk attachment, otherwise do this in a separate bowl with a handheld mixer. Beat the egg whites until fluffy, then fold the egg whites into the batter.
Pour into the pan and bake on center rack for 35 to 40 minutes (may take up to 45). Place on a wire rack and let cool.
Meanwhile, poke holes in the warm cake with a skewer spacing about ½ inch apart. Combine the condensed milk and coconut milk and pour over the cake, very gradually, allowing mixture to drip down into the holes. When cool, cover and chill the cake for at least two hours.
Make the topping. In a large bowl, beat the cream until thick. Add the sugar and beat until stiff peaks start to form. Beat in the vanilla. Spread or pipe over the cake and sprinkle with toasted coconut. Serve directly from the pan.
Notes
You can use all-purpose, just weigh out 250 grams, which is about 2 very lightly spooned cups.