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Beat eggs in top of a double boiler on medium speed of an electric mixer until frothy.
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Combine sugar, flour, and salt; stirring well; gradually add to eggs, beating until thick.
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Gradually stir about one-fourth of hot milk into egg mixture; add remaining milk, stirring constantly.
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Bring water in bottom of double boiler to a boil.
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Reduce heat to low; cook, stirring occasionally, 20 minutes, or until custard thickens and coats a metal spoon.
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Stir in vanilla.
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Pour custard into serving bowl and chill.