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Line two loaf pans with tin foil. Grease the foil with butter or coconut oil to prevent sticking. Set off to the side.
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Take the quart of ice cream out of the freezer so it will become slightly melted.
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In the bowl of a stand mixer fitted with the paddle attachment, beat together the butter and sugars until creamy and smooth, about two minutes.
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Add the vanilla and milk, mix until combined.
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Add the flour and cocoa powder all at once. Mix on low until no bits of flour are visible.
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Transfer half of the cookie dough to each prepared pan. Press into one even layer. It is ok if it does not reach the edges. Chill the cookie dough for an hour while the ice cream is melting.
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Remove prepared pans from fridge. Add ice cream to one pan, right on top of the cookie dough layer. Spread in one even layer over the cookie dough. Gently remove the cookie dough from the other pan. Press it right on top of the ice cream, making sure not to press too hard to squeeze all the ice cream out.
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Chill the sandwiches in the freezer overnight.
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When ready to serve, flip the loaf pan over on to a cutting board. Gently remove the foil. Cut the large rectangle in half width wise. Then cut each half in half again, diagonally to make triangle sandwiches. Drizzle each sandwich with a little bit of salted caramel sauce and then serve.