Prepare cake per box directions for 2 layer cake using 9" pans.
Allow to cool.
Line 9" pan with aluminum foil and spread slightly softened ice cream into pan.
Place in freezer for 2 hours.
Crush each type of cookies in food processor. Then mix together in large bowl.
Beat butter until creamy. Slowly add in powdered sugar and vanilla.
Add milk as needed to achieve spreading consistency.
Line a baking pan (that will fit in freezer) with parchment paper.
Frost one side of one of the cakes and sprinkle with crushed cookie mixture.
Place that cake, frosting side down, in center of prepared pan.
Remove ice cream from freezer; remove from pan and remove foil.
Place ice cream disk on top of cake on prepared pan.
Place remaining cake on top of ice cream layer.
Frost all three layers with icing, covering completely.
Sprinkle crushed cookies over frosting and gently press in place.
Place cake in freezer for at least 2-3 hours.
You can optionally garnish with whipped topping and strawberries.