Preheat the oven to 350F/177C. Line two, 8-inch (20-cm) round cake pans with parchment paper without greasing the sides. Place the eggs, sugar and vanilla into mixer bowl and whisk on high speed for 7 to 9 minutes, until the eggs are thick and pale, almost white in color.
In a separate bowl, combine the flour and baking powder. Sift the flour into egg mixture in small batches, folding very gently but thoroughly after each addition until all flour is added. Divide the cake batter evenly between the prepared pans.
Bake in preheated oven for 18 to 20 minutes, until the tops are golden brown. Remove the cakes from the oven and run a knife along the edges of the pan to release it from the sides. Allow the cake layers to cool in the pan for a few minutes, then let them cool on a wire rack. Let the layers cool completely before slicing in half with a long serrated knife.
Next, prepare the frosting. In a large bowl, whisk the softened cream cheese for a few minutes until it's smooth and creamy. Add the chilled heavy cream, sugar and into mixer bowl. Whisk on high speed until stiff peaks form, about 3 to 4 minutes.
Wash, pat dry and thinly slice the strawberries. To assembled cake, spread a layer of sliced strawberries over sponge cake and cover with generous amount of frosting. Repeat for remaining layers. If desired, soak the sponge cake layers with a simple syrup or strawberry syrup. Arrange more strawberries on top in a decorative pattern. Refrigerate the cake until ready to serve.