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Line two small sheet pans or 8-inch cake pans that will fit into your freezer with foil. Set aside.
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In a large bowl, beat the heavy cream until stiff peaks form. You want it to be slightly over-whipped. Then, stir in the condensed milk, vanilla extract, brown sugar, and salt until combined. Fold in the mini chocolate chips until well distributed.
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Divide the ice cream between the two cake pans, and spread evenly. It should be about 3/4 inch thick, but does not have to be perfect. In a small bowl, stir together the dulce de leche and the remaining 2 tbs. of heavy cream. Then, dollop the mixture all over the top of the ice cream in both pans, and use a knife to swirl it into the ice cream. Freeze both pans of ice cream until solid, about 2 hours.
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Remove from the freezer, and use the foil to pull the ice cream out of the cake pan, working with only one pan at a time so it doesn't melt too quickly. Using a round cutter that is slightly smaller than your cookies, cut out rounds of ice cream, and sandwich between two cookies, pressing together slightly.
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You want to work in small batches here, and move quickly so the ice cream doesn't melt too fast! Wrap each sandwich tightly in plastic wrap or place into individual zipper bags and freeze immediately. Enjoy!