Soak the pearl tapioca in cool water for 30-40 minutes. Drain any unabsorbed water from the tapioca.
Combine the tapioca, milk, half and half, and salt. Bring to a low simmer over medium heat stirring almost constantly. Reduce the heat to low and slowly add the sugar stirring constantly. Cook until the pearls are plumped and the pudding has slightly thickened, stirring constantly; approximately 5-7 minutes. Scrape the bottom of the pan.
Remove the tapioca from the heat. Using a large spoon add 2-3 tablespoons of the hot tapioca mixture to the beaten eggs in a small bowl and whisk vigorously to combine. Do this several times to ensure that the beaten eggs warm.
Return the pan to medium low heat and slowly add the egg mixture. Cook (but do not boil) until thickened to pudding consistency stirring constantly; approximately 3-5 minutes. Scrap the bottom of the pan to prevent anything from burning.
Remove from the heat. Wait 1-2 minutes and stir in the vanilla. Continue to stir frequently while it cools to prevent a skin from forming. Serve warm or cover with plastic wrap to further prevent a skin from forming.
