Whisk milk, cream, sugar, and salt together in a medium saucepan over medium heat. Cook, stirring occasionally, until the liquid barely comes to a simmer.
Stir in the tapioca pearls and immediately reduce the heat all the way to the lowest setting. Continue to cook and stir for 45 to 60 minutes until the tapioca pearls are translucent and soft and the mixture has begun to thicken. Please note that different types and brands of tapioca may require shorter cooking times.
Whisk the eggs in a medium bowl. Add 1/2 cup of the hot tapioca mixture, stirring well. Add another 1/2 cup of the hot liquid, stirring again, before combining the tempered egg mixture back into the saucepan with the tapioca and milk mixture.
Continue to cook 1 to 10 minutes, until thickened to your liking. Remove from heat and stir in the vanilla extract. Cool for at least 20 minutes before pouring into individual serving cups. Serve warm or cover with plastic wrap directly in contact with the top of the tapioca to prevent it from forming a skin and chill to serve cold.