To make the ice box cake:
Line an 8 by 4-inch loaf pan with plastic wrap, set aside.
To make the caramel whip cream:
In a medium-large saucepan put the sugar in a mound in the center of the pan, be sure it doesn't hit the sides. Gently add the water and corn syrup, making sure the sugar doesn't splash up on the sides of the pan. If any of the sugar is not dissolved very gently stir, but make sure none of the sugar hits the sides of the pan. (All of this care to keep the sugar off the side of the pan will prevent your sugar from crystalizing while it cooks.) Cook over high heat, without stirring. When the sugar starts to color on the edges, gently stir the sugar. Until it is quite dark, it will smoke a bit.
Once the caramel is dark in color, reduce the heat and add half the cream. The caramel will sputter and sieze up, which is normal. Gently whisk the caramel until the sugar dissolves. Add the remaining cream and stir.
Strain the caramel cream into a shallow container. Cover and refrigerate until well chilled.
Using a whisk or stand mixer whip 2/3 of the chilled caramel cream until soft peaks. Reserve the remaining 1/3 of the cream for topping the cake.
Coat the bottom of the prepared pan with about a 1/4-inch-thick layer of the cream. Line the outside of the pan with the cookies. Spread a layer of the cream on each cookie and layer them together in the pan. You should end up with about 3 rows of cookies and cream.
Cover the top with more of the cream so the cookies are completely covered. Refrigerate the cake for at least 3 hours or overnight. Invert the cake onto a serving platter.
Whip the remaining 1/3 of the cream and decorate the cake as you wish.
Cream together the butter, sugar, brown sugar and vanilla until light, about 2 minutes.
In a medium bowl, whisk together the flour, cocoa powder, soda and salt. If there are any lumps of cocoa powder, sift the dry ingredients before adding to the butter.
Add the dry ingredients to the butter mixture and mix just to combine. Add the milk and mix just to combine.
Form the dough into two 1 1/2-inch-thick logs. Wrap well in plastic wrap and refrigerate for at least an hour.
To bake: Preheat the oven to 350 degrees F and line 2 baking sheets with parchment.
Slice the log of cookie dough into 1/8-inch-thick coins.
Arrange on the baking sheets with about 1 1/2 inches between the cookies. Bake for 8 minutes and then rotate the trays back to front and switch from top and bottom racks. Bake for another 2 minutes or until they are dry looking and firm. Because the cookies are so dark, you can't go by color on these.