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Spread 2 cups of the cookie dough in an even layer in the prepared pan, pressing down with your fingers until the layer is completely flat. Cover with parchment paper and freeze for 2 hours. Remove the cookie dough layer from the pan and transfer to the freezer.
Repeat with the remaining 2 cups cookie dough, but do not remove the frozen second layer from the pan.
Soften the ice cream until it is easy to work with (but not melted). Using a spatula, spread the ice cream in a smooth, even layer on top of the cookie dough layer in the pan.
Remove the other cookie dough layer from the freezer, flip it upside down and place on top of the ice cream layer (so the side that you pressed down on with your fingers is touching the ice cream). Press down so the three layers are tight and touching--this will help ensure the ice cream is spread evenly. Cover with parchment and freeze until frozen very hard, at least overnight.
Lift the layers out of the pan, remove the parchment and clean up the edges with a knife. With a large chef's knife, cut into squares or your desired shape (if difficult to cut, run the knife under warm water). Wrap the sandwiches in parchment paper and tie or tape the edges. Store in the freezer for up to 3 months.
Special equipment: Parchment paper, 8x8 or 9x9 pan with square corners (square corners are important!), Rubber spatula, Chefs knife