Fill a medium pot full with water and bring to a boil. Once boiling, add in the tapioca pearls and give it a stir. Boil for 15 minutes until the tapioca is mostly translucent with a tiny dot of white in the middle. Cover, remove from the heat, and let sit for 10 minutes until the tapioca are completely translucent.
Drain the tapioca pearls in a fine mesh sieve and keep submerged in cold water until ready to use.
In a medium mixing bowl, whisk together eggs, sugar, cornstarch, and vanilla extract. Set aside.
In a small pot, heat milk on medium heat until small bubbles start coming to the surface and it just starts simmering. Slowly pour the hot milk into the egg mixture while whisking quickly and constantly with your other hand to temper the eggs.
Pour the entire mixture back into the pot and return it to low-medium heat. Continue whisking the mixture constantly until it thickens into a custard consistency, about 8-10 minutes.
Remove the custard from the heat. Add the drained tapioca pearls and stir to combine. Transfer this whole mixture to an 8-9" baking dish.
Preheat the oven to 375°F.
Take your rolled out crust topping out of the fridge and peel off the parchment paper. Place the dough on top of the tapioca in the baking dish. Use a knife to trim off any overhanging excess.
Use a knife to score a diamond pattern on top of the crust. Brush a light layer of beaten egg on the crust.
Bake for 35-40 minutes or until the crust is golden brown. Let the baked tapioca pudding cool on a wire rack for at least 20-30 minutes so the filling can set before serving warm.