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Combine milk and cream in medium saucepan.
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Bring just to simmer.
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Remove from heat.
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Place sugar in large saucepan.
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Stir over medium heat until sugar melts (some soft lumps will remain) and is deep brown, about 5-7 minutes.
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Stir the sugar continuously while it melts.
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Whisk in hot milk mixture.
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Stir over low heat until caramel bits melt, about 5 minutes (mixture may look curdled).
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Whisk yolks in large bowl to blend.
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Gradually whisk in brown sugar mixture.
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Return mixture to saucepan.
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Stir over low heat until custard thickens and leaves path on back of spoon when finger is drawn across, about 5-7 minutes (do not boil).
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Cool.
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Mix in vanilla.
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Puree custard in batches in blender until very smooth.
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Refrigerate until cold, at least 1 hour or overnight.
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Process custard in ice cream maker according to manufacturers instructions.
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Transfer to container; cover and freeze until firm.