Preheat the oven to 350 degrees F (175 degrees C). Grease a 10×15-inch baking dish.

Make the cake: Beat egg whites in a large mixing bowl with an electric mixer on high speed until stiff peaks form. Gradually beat in sugar until mixture is glossy. Beat in egg yolks, one at a time, beating well after each addition. Reduce the speed to medium and mix in flour, about 1 tablespoon at a time. Mix in milk, baking powder, and vanilla. Pour batter into the prepared baking dish.

Bake in the preheated oven until lightly browned on top and a toothpick inserted in the center comes out clean, about 25 minutes. Remove from the oven and let cool for 15 minutes.

Make the tres leches: Combine condensed milk, evaporated milk, and cream in a blender. Pulse several times until well blended.

Pour tres leches over cake. Cover and refrigerate until cake is cold and all liquid has been absorbed at least 1 hour.

Cut chilled cake into 12 squares. Top each serving with a dollop of whipped cream and a few sliced strawberries.