Preheat an oven to 350 degrees F (175 degrees C). Grease and flour two 10x15 inch jelly roll pans.
Beat the eggs until combined; stir in the melted butter. Add the water, pudding mix, and yellow cake mix, stirring well to combine. The batter will be very thick. Divide the batter between the prepared pans, spreading it evenly.
Bake until the cakes spring back when pressed lightly with a finger or a tester comes out clean, 15 to 20 minutes. Cool completely on wire racks.
To make the filling, combine the room-temperature butter, cream cheese, and confectioners' sugar. Beat until smooth. Stir in the whipped topping and vanilla extract.
When the cakes are cool, spread the filling mixture on top of one cake layer. Place the second cake layer on top of the first, and cut into bars. Wrap each bar in plastic wrap and store in the freezer.
