Bake the layers. Fold the cookie crumbs into the mixed batter and bake in two greased 8 inch pans at 350 degrees F for 25 to 30 minutes. Cool completely, about 1 hour.
Bake the crumble. Toss the flour, sugar, cinnamon, and salt with the melted butter, bake on a lined sheet for 8 to 10 minutes until set, and cool.
Make the filling. Beat the butter with the powdered sugar, cinnamon, vanilla, and salt, then stir in the cookie crumbs and cooled crumble, adding milk until spreadable.
Whip the buttercream. Beat the butter pale, add the powdered sugar gradually with the vanilla, cinnamon, and salt, and loosen with the cream.
Assemble. Fill between the layers, frost the top and sides, and finish with halved cookies. Chill for 20 minutes for clean slices.