Check whether your tapioca pearls require soaking. If needed, soak them according to the package instructions, then drain well. Do not soak instant tapioca or products that specifically say soaking is unnecessary.
Lightly grease the inside of your slow cooker if recommended by its manufacturer. Add the tapioca pearls, milk, sugar, and salt. Stir thoroughly so the pearls are distributed evenly throughout the milk.
Cover and cook on LOW for approximately 2–3 hours. Cooking times vary by slow cooker and tapioca brand, so begin checking the texture after about 1½ hours.
Stir gently about every 30 minutes, scraping the bottom and sides to prevent the milk from sticking. Keep the lid on between stirring sessions to maintain a steady temperature.
The pudding is ready for the next step when the pearls are mostly translucent and tender, with no hard or chalky centers. If they are still firm, continue cooking and check again after 15–20 minutes.
In a separate heatproof bowl, whisk the egg yolks. Slowly whisk about ½ cup of the hot pudding mixture into the yolks, adding a little at a time. This gradually warms the eggs and helps prevent scrambling.
Slowly stir the tempered egg mixture back into the slow cooker. Cook on LOW for another 10–15 minutes, stirring frequently, until the pudding thickens and reaches 160°F (71°C) or higher. Do not allow it to boil vigorously.
Turn off the slow cooker and stir in the vanilla extract. Taste carefully once cool enough and adjust the sweetness if needed.
Let the pudding stand for 10–15 minutes. It will continue to thicken as it cools. If it becomes too thick, stir in a small amount of warm milk until the desired consistency is reached.
Spoon the pudding into individual bowls or dessert cups. Serve warm, or cool it promptly in shallow containers and refrigerate. For chilled pudding, cover and refrigerate until cold, then garnish with berries, cinnamon, or whipped cream.