Preheat the oven to 375 degrees F. Grease bottom only of a 15x10 inch jellyroll pan and line bottom with parchment paper.
Beat eggs in the bowl of a stand mixer fitted with a whisk attachment for five minutes. Gradually beat in sugar, beating for another 2-3 minutes. While the mixer is going, sift together the dry ingredients (flour, baking powder and salt).
Reduce mixer speed to medium low and beat in water and vanilla.
Remove bowl from stand and fold in the flour mixture. Batter should be fairly liquid and bubbly.
Pour into the pan and bake for 12-15 minutes or until toothpick inserted comes out clean. Loosen edges from pan with a knife and let cool in pan for about 10 minutes. Invert onto a flat surface. Peel away parchment paper, then invert again onto a large cooling rack. Cool completely. Freeze for about an hour to make carving easier.
Prepare the whipped cream filling. Beat the cream until stiff peaks just start to form, then beat in confectioners’ sugar and vanilla (don't overbeat). Keep chilled while you carve the cake.
Line the inside of a 9x13 inch pan with plastic wrap leaving a couple of inches of overhang.
To carve, put the cake on a cutting board. Cut it in half so that you have two 10x7 ½ inch rectangles. Take one of the rectangles and split it into two uneven layers, one very thin and one thick. Repeat with the second rectangle. You should end up with two thin layers and two thick layers total.
Put one of the thin layers of cake in the bottom of the lined pan and spread a thin layer of sundae topping over it. Top it with the second thin layer of cake. Spread a layer of whipped cream over the cake, then arrange strawberry slices evenly over the whipped cream. Spread a little more whipped cream over the strawberries, then lay one of the thick layers of cake over it, cut side up. Spread strawberry topping over that layer of cake, then add a layer of strawberries and whipped cream. Top with remaining thick layer of cake. Cover cake with plastic wrap and chill while you make the topping.
To make the cream cheese topping, beat the 1/2 cup of heavy whipping cream JUST until stiff peaks form (don’t overbeat). Set aside. In another bowl, beat the cream cheese (or mascarpone), confectioners’ sugar and vanilla until smooth. Fold the lightly whipped cream into the cream cheese mixture. Spread across top of the cake, reserving some of it to pipe rosettes if desired. Run a cake comb or a fork through the top to make stripes.
Chill for 4 to 6 hours or until ready to serve. To serve, lift from the pan and cut into squares. Garnish each square with a rosette (or just a blob) of frosting and a strawberry half.