For the cake:

Make the frosting: Put the white chocolate in a microwave-safe bowl and microwave in 30-second intervals, stirring, until smooth; let cool slightly. Beat the butter, vanilla and salt in a large bowl with a mixer on medium-high speed until smooth, about 1 minute. Add the melted white chocolate and beat until combined. Gradually beat in the confectioners' sugar until smooth.

Assemble the cake: Place 1 cake layer on a platter; spread 1 cup frosting on top and sprinkle with 1/2 cup chopped cookies. Top with the second cake layer. Cover the whole cake with the remaining frosting, then press the remaining cookies into the sides. 

Basic Vanilla Cake:

Preheat the oven to 350 degrees F. Butter two 9-inch-round cake pans and line the bottoms with parchment paper; butter the parchment and dust the pans with flour, tapping out the excess.

Whisk 3 cups flour, the baking powder and salt in a bowl until combined. Beat 2 sticks butter and the sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Reduce the mixer speed to medium; beat in the eggs, one at a time, scraping down the bowl as needed. Beat in the vanilla. (The mixture may look separated at this point.)

Mix 1/2 cup water with the cream in a liquid measuring cup or bowl. Beat the flour mixture into the butter mixture in 3 batches, alternating with the cream mixture, beginning and ending with flour, until just smooth.

Divide the batter between the prepared pans. Bake until the cakes are lightly golden on top and the centers spring back when pressed, 25 to 30 minutes. Transfer to racks and let cool 10 minutes, then run a knife around the edge of the pans and turn the cakes out onto the racks to cool completely. Remove the parchment. Trim the tops of the cakes with a long serrated knife to make them level, if desired.