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Scald the milk in the microwave or in a small saucepan on the stovetop. Microwave works best as there is no chance of burning the milk. bring the temperature to just under boiling point.
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Meanwhile, in a saucepan combine the flour, sugar and salt.
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Over medium flame slowly add about the 1/3 of the scalded milk whisking constantly. Continue to cook over medium heat until mixture begins to slightly thicken.
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Add the next 1/3 of the milk until it slightly thickens again,then repeat with the final 1/3 of the scalded milk.
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At this point remove from heat and pour about a half cup of this mixture onto the beaten eggs, whisking constantly.
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Pour the egg mixture immediately back into the pot, continuing to constantly stir.
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Cook for an additional minute or two until pudding consistency and remove from the flame.
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Stir in the butter and vanilla extract.
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Cool completely in the fridge.