Whisk the milk, sugar, vanilla extract, salt, and tapioca pearls in a slow cooker until the sugar has dissolved. Turn the cooker to high setting, cover with lid, and cook for 2 hours. (If preferred, set on low setting and cook for 4 hours. Stir pudding occasionally during cooking.)
Place egg yolks into a bowl, and whisk until smooth.
Mix about 1 tablespoon of the hot pudding into the egg yolks until thoroughly combined; continue gradually mixing hot tapioca pudding into the egg yolks, slowly increasing the amount of pudding mixed in, until the yolks and pudding total about 2 cups. Slowly pour the yolk mixture into the pudding in the slow cooker until blended, whisking constantly until the egg yolks have thickened the pudding, about 5 minutes.
Place lid back on the cooker, and continue cooking until the pudding is your desired degree of thickness, on high setting for about 30 more minutes (or low setting for 1 more hour).
