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In a large measuring cup with a pour spout, add 1 cup of milk. Set milk and a silicon spatula next to the stovetop.
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In a medium bowl whisk egg yolk with 1/4 cup of milk until well combined. Set next to the stovetop.
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In a small bowl whisk flour and sugar with 1/4 cup of the milk until smooth. Set next to the stovetop.
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Add the flour mixture to the pan and bring the pudding to a very slow simmer.
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Simmer, whisking for 2 minutes to thicken and then decrease heat to medium-low so the pudding is no longer simmering.
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Ladle 1/4 cup of the hot pudding into the egg yolk mixture and whisk rapidly. Repeat.
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Add the egg yolk mixture back to the saucepan.
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Raise the heat slightly and continue stirring the pudding until it thickens to the point that it thickly coats the back of the spatula, approximately 2-4 minutes. Do not boil.
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Remove the pudding from the heat and stir in the butter, vanilla, vanilla bean and salt until the butter is melted.
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Strain pudding through a single mesh strainer if desired.
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Pour pudding into a heat-proof bowl and press a piece of plastic wrap directly on the surface of the pudding.
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Let cool and then refrigerate at least 2 hours.