Pour tapioca pearls into the milk and let sit, covered, overnight in the refrigerator (some brands may not require pre-soaking).
After soaking, pour the tapioca/milk mixture into a medium saucepan. Add the remaining ingredients and stir to combine.
Heat on medium, stirring periodically and making sure nothing sticks on the pan bottom. When mixture starts to thicken, stir continuously.
When mixture has thickened noticeably, but before it comes to a boil remove from heat. Pour into a covered bowl and chill (at least somewhat). May be served warm or cool.
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Notes
Some brands of pearl tapioca require soaking first, others do not. To be safe, I just make a habit of doing this. I have tested with Reese brand and Frontier brand (organic). If using a vanilla bean, split the pod, scrape the seeds out, and add both seeds and pod to the pot instead of the teaspoon of vanilla. When the pudding is done cooking, remove and discard the pod. Many recipes add the egg later and temper it. In recipes with cooked egg, I usually find that it is easiest to add the egg(s) right away to cool ingredients and skip the tempering (which is more work and error prone). You need to stir regularly for this to work, but the pearls will gum up/stick to the pan bottom if you don’t stir regularly anyway.
I am not a health professional and nutrition data is calculated programatically. Accuracy may vary with product selection, calculator accuracy, etc. Consult a professional for the best information.