Heat the oven to 350F and grease a 9x13 baking dish. Whisk the flour, baking powder and salt together.
Beat the egg yolks with 3/4 cup of the sugar until pale and thick, then stir in the whole milk and vanilla.
In a clean bowl, whip the egg whites to soft peaks, add the remaining 1/4 cup sugar, and continue to stiff, glossy peaks.
Fold the flour mixture into the yolk mixture, then fold in the whites in three additions, stopping the moment the streaks disappear.
Pour into the dish and bake 25 to 30 minutes, until a skewer comes out clean and the top springs back.
Whisk the evaporated milk, sweetened condensed milk and 1/2 cup of the heavy cream together.
Pierce the warm cake all over with a fork, then pour the milk mixture over it in three stages, waiting a few minutes between each so it soaks in rather than pooling.
Cover and refrigerate at least 4 hours or overnight. Before serving, whip the remaining cream and spread it over the top.