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Place egg yolks in a separate bowl and set side.
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In a medium saucepan, add the flour, sugar, and salt and whisk to combine.
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Add the milk, Kailua, and vanilla extract.
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Heat the mixture over medium-low heat, whisking constantly.
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Once the mixture is warm (but not boiling) pour about 1/4 c. of it into the bowl with the egg yolks and whisk vigorously to temper the yolks.
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Immediately pour the egg yolk mixture back into the saucepan and continue whisking over medium-low heat to prevent the eggs from cooking.
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Whisk until the pudding starts to thicken, then add chocolate chips and continue whisking until the pudding starts to thicken.
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Pour the pudding into a medium bowl and cover with clear plastic wrap (directly on the pudding surface), then poke a few holes in the plastic wrap with a toothpick.
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Allow the pudding to cool on the counter for at least 1 hour before refrigerating.
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Refrigerate 2-3 hours until the pudding has cooled and is firm.