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In a small bowl, mix together 1/4 cup of the milk and the cornstarch to form a slurry. Set aside.
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Next, in a sauce pan, whisk together the remaining milk, cream, sugar, salt, and corn syrup and bring to a boil over medium-high heat, stirring frequently. Cook for four minutes.
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Stir in the cornstarch slurry and return the mixture to a boil, then cook for approximately 2 more minutes.
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In a separate bowl, add 1/4 cup of the warm cream mixture to the cream cheese and whisk until smooth.
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Mix in the remaining cream mixture.
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Prepare a large ice bath.
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Pour the warm cream mixture into a large freezer bag, seal the bag tightly, and place in the ice bath until cool.
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Transfer the ice cream mixture to your ice cream maker and add in half of the crushed oreos.
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Process according to your machine's directions (I find this usually takes about 25-30 minutes).
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At the end of processing, add the remaining oreos and mix for 30 seconds or so to incorporate.
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Transfer to a freezer safe container and let set for a few hours or enjoy immediately.