Preheat oven to 350°F (175°C) and butter a 9x13-inch baking dish. Whisk the flour, baking powder, and salt together. Beat egg whites with ¼ cup sugar to stiff peaks. In another bowl, beat egg yolks with ¾ cup sugar until thick and pale; stir in milk and 1 tsp vanilla. Fold in the dry ingredients, then the egg whites gently. Spread batter in the pan and bake 25 to 30 minutes until golden and springy. Cool 10 minutes.

Whisk together evaporated milk, condensed milk, ½ cup whole milk, and remaining 1 tsp vanilla. Poke the warm cake all over with a skewer, then slowly pour the milk mixture over the top. Let it soak for 30 minutes at room temperature, tilting the dish to help it distribute.

Beat the heavy cream, 2 tablespoons sugar, and ½ teaspoon vanilla until soft peaks form. Spread the cream over the soaked cake, cover, and refrigerate at least 4 hours or overnight.

Remove the cake from the fridge, run a knife around the edges, and slice into squares. Plate each piece with the cream layer on top, dust with cinnamon, and serve cold.