Using the back of a wooden spoon, poke at least 3 rows of 4 holes in the cooked cake, making 12 holes total.
In a large bowl, add the packet of cookies and cream pudding mix and the milk and whisk until there are no lumps. Add the whipped topping and the crushed chocolate cookies. Stir until well-combined and set aside.
Pour the sweetened condensed milk over the cake and let settle into the holes for about 10 minutes. Some of the mixture will still stay on top, which is okay.
Spread the pudding mixture mixture and smooth it out evenly. Sprinkle extra crushed cookies on top. Chill the cake for at least 3 hours or up to overnight.