Preheat oven to 350°F (180°C). Liberally grease two 8″round cake pans with vegetable shortening, and/or spray with baking spray.
Combine flour, sugar, baking powder, salt, and pudding mix in a large mixing bowl. Add in water and eggs, beating just until smooth. Carefully add melted butter and vanilla to the batter, mixing on medium speed until smooth.
Divide batter evenly into two bowls. Add cocoa powder to one bowl, stirring until evenly distributed.
Divide batter among prepared cake pans, one flavor per pan. Bake until golden and knife inserted into center of batter comes out clean and cake springs back – about 45-60 minutes.
Allow to cool 10-15 minutes before turning cakes out onto baking rack to cool fully. Ideally, allow to cool to room temperature, wrap tightly with plastic wrap. Allow cake to sit overnight.
Prepare Swiss meringue buttercream. Run about 1/3 of the Oreo cookies through a food processor until finely ground. Crush another 1/3 of the package by hand, yielding medium/large chunks of cookies. Add cookie powder to frosting, stirring until well combined. Add cookie chunks, to taste – as many as you’d like.
To Assemble Cake
Remove plastic wrap from cake layers. Carefully slice the domed top off each round, leveling the surface of the cake. Carefully cut each cake in half, horizontally, for 4 thin rounds of cake in all.
Place one round of chocolate cake on cake plate, spread with buttercream. Top with a round of vanilla cake, spread with buttercream. Top with second round of chocolate cake. Spread with a final layer of buttercream, and top with remaining layer of cake.
Frost sides and top of cake with remaining buttercream. Garnish with remaining cookies, if desired. Serve at room temperature.
Note: This cake gets VERY hard when chilled. Always serve cakes at room temperature! Cold cake is DRY cake.