Butter the bottom and sides of a 9x13 inch baking dish, line the bottom with parchment paper then lightly butter the parchment paper.
Place oven rack in center of oven. Preheat the oven to 350 degrees.
Combine flour, baking powder, and salt in a large bowl. Separate eggs.
Beat egg yolks with 3/4 cup sugar on high speed until yolks are pale yellow, about 2 minutes. Stir in the 1/3 cup milk and vanilla. Pour the egg yolk mixture over the flour mixture and stir very gently until combined.
Using electric beaters, beat egg whites on high speed until soft peaks form. Gradually add the remaining 1/4 cup sugar and beat until egg whites are stiff but not dry.
Fold egg white mixture into the batter very gently until just combined. Pour into the prepared pan and spread to even out the surface.
Bake for 25 to 30 minutes or until a toothpick comes out clean. Let cake cool for 10 minutes and then invert cake onto a rack to cool and remove parchment paper. Once cool, return to the baking dish.
In a medium bowl, combine the 1/3 cup of heavy whipping cream, condensed milk, and evaporated milk with a pinch of salt. Mix well.
Using a toothpick or fork poke holes all over the cake. Slowly pour the milk mixture all over cake starting at edges. It may take a minute to absorb the milk. Cover with plastic wrap and refrigerate for at least 1 hour or up to overnight to allow the cake to fully absorb the milk.
Make the whipped topping by beating the heavy cream, powdered sugar, and vanilla until stiff peaks form, about 3-4 minutes. Smooth over the top of the cake.
Combine the mixed berries in a bowl with 1 teaspoon of sugar and spread on the top of the cake.
Cut into squares and serve.
Keep leftovers refrigerated. It still tastes great for up to 3-4 days later.