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Combine sugar, cornstarch and salt in a medium saucepan.
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Whisk in about 1/3 cup of the half-and-half, until smooth.
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Whisk in the remaining half-and-half until well combined.
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Cook over medium heat, stirrying constantly and gently until thickened (about 5 minutes, but the time will vary).
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Reduce heat to low and continue to heat, stirring gently until the mixture reaches a simmer.
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Cook one minute more over low heat, not stirring, then remove from heat.
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Fold in vanilla and pour pudding into 4 serving dishes.
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The book doesn't say, but I presume that you could serve this either warm or chilled.