Preheat oven to 350°F. Grease a 9x13 inch baking pan.
Separate eggs. Place whites in a large bowl and yolks in a separate bowl.
Beat egg whites to soft peaks, then gradually add ¼ cup sugar. Beat to stiff, glossy peaks.
Beat egg yolks with remaining ¾ cup sugar until thick and pale, about 3 minutes. Mix in vanilla and whole milk.
Sift flour, baking powder, and salt into the yolk mixture. Fold gently until just combined.
Fold in whipped egg whites in three additions, using a gentle hand to preserve the air.
Pour batter into prepared pan and spread evenly. Bake 22 to 25 minutes until golden and toothpick comes out clean. Edges should pull slightly from the pan.
Cool cake in pan for 15 minutes. Poke holes all over the surface with a skewer or fork.
Whisk together condensed milk, evaporated milk, heavy cream, and strawberry puree until smooth.
Pour milk soak slowly and evenly over the entire surface of the cake, making sure to reach the edges.
Cover with plastic wrap and refrigerate a minimum of 4 hours, or overnight.
Beat cold heavy cream with powdered sugar and vanilla to firm peaks.
Spread whipped cream over chilled cake. Top with sliced strawberries and whole berries. Dust with powdered sugar. Serve cold.