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Cookie Dough: Beat the butter and the sugar together until light and fluffy, 2 mins.
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Beat in the salt and then alternate adding the flour and the milk until just combined.
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Stir in the vanilla extract and chocolate chips.
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Line a sheet tray with wax or parchment paper. Drop teaspoons of the cookie dough onto the prepared sheet. Cover and chill for at least an hour or overnight.
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Ice Cream: Stir the sweetened condensed milk and the vanilla together in a large bowl.
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In a separate large bowl, whip the heavy cream until you have stiff peaks.
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Fold the whipped cream into the condensed milk and vanilla. Then gently fold in the chocolate chips and cold cookie dough chunks.
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Scrape into two loaf pans, cover with plastic wrap and freeze until firm, at least 5 hours or overnight.