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Chill a medium mixing bowl and the beaters of an electric mixer.
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In the bowl, beat the cream cheese at medium speed until soft and smooth.
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Gradually add the sugar, 1/4 cup at a time, beating well after each addition.
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Beat in the sour cream and then the whipping.
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cream.
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Add the salt, lemon juice and vanilla and beat the mixture just until thick and smooth.
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Cover and refrigerate overnight.
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Wash and dry the mixer beaters and chill them again.
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The next day, using the chilled beaters and gradually increasing the mixer speed from low to medium, beat the cold ice cream mixture until loose and creamy, about 3 minutes.
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Pour into an ice cream maker and freeze according to the manufacturer's instructions.
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Serve immediately, or pack the ice cream into a covered container and freezer for up to 24 hours. Allow the ice cream to soften in the refrigerator for 20 to 30 minutes before serving if frozen overnight.