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In a saucepan, stir together the sugar, flour, and salt until well-combined. In a bowl, whisk the egg yolks until smooth, then slowly whisk in the milk. Slowly, whisk the milk mixture into the dry ingredients until no lumps remain. Add the cold butter and cook over medium heat, stirring constantly to prevent scorching, until the pudding thickens and begins to boil. Remove from heat and stir in the vanilla. Cool to room temperature.
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