Preheat oven to 325° F. Grease 9x13 glass or ceramic baking dish. Set aside.
In a medium bowl, whisk flour, baking powder and salt. Set aside
In the bowl of a stand mixer (or using a hand mixer), beat the egg whites until stiff. Continue beating and gradually add the sugar until the sugar dissolves and the whites are thick and shiny. With the mixer on low, add egg yolks, one at a time, then vanilla.
Mix on low speed for 3 minutes. Beat in the flour mixture alternately with the milk until the batter is smooth.
Transfer the batter into the prepared pan. Bake at 325° F for 40 to 45 minutes or until a toothpick inserted in the center of the cake comes out clean.
Remove the cake from the oven and cool in the pan on a rack to lukewarm, about 20 minutes. Meanwhile, make the sauce.
Sauce
In a large bowl, thoroughly whisk all the sauce ingredients together.
After the cake is cooled a bit, but is still slightly warm, poke the top all over with a skewer or fork. Be generous with making the holes.
Gradually spoon the sauce over the cake and leave it to soak 30 to 40 minutes at room temperature. Then cover and refrigerate at least 3 hours and up to 24 hours.
Toppings and Assembly
When ready to serve, prepare the toppings. Place sliced strawberries in a bowl and toss to combine. Let the mixture sit for 10 minutes so strawberries release their juices.
Make the whipped cream. In a cold metal bowl with an electric mixer, whip the cream and sugar to soft or stiff peaks, as preferred. Mix in vanilla.
Cut the cake in squares and serve cold topped with sweetened whipped cream and strawberries.
Notes
Egg whites: It's essential that stiff peaks form in order to make a light and airy texture in the cake. The easiest way to do this is to use an electric mixer with a whisk attachment.Rum: If you prefer to not use alcohol, omit the rum. Alternatively, you can substitute it with 2 Tablespoons espresso or 1 Tbs vanilla extract.Store covered in the refrigerator for up to 3 days.Freeze cake, unassembled, for up to 3 months. Defrost in the refrigerator before adding toppings and serving.