Begin by placing the tapioca pearls into a clean bowl. Submerge them in water, ensuring they are fully covered.

Agitate the water with a gentle stirring motion and then promptly drain the water.

Refill the bowl with fresh water, ensuring the pearls are submerged. Allow the pearls to soak for a minimum of seven hours, extending up to an overnight duration if so desired.

Once the soaking process is complete, proceed to drain the tapioca pearls thoroughly and set them aside.

In a large saucepan, combine the whole milk and 3/4 cup of granulated sugar. Stir until the sugar begins to dissolve.

Place the saucepan over medium heat and bring the milk and sugar mixture to a simmer, being watchful for small bubbles forming around the perimeter of the pan.

Upon reaching the simmering point, add the pre-soaked and drained tapioca pearls to the saucepan. Reduce the heat to maintain a consistent simmer.

Continue simmering the mixture for approximately 25 minutes, or until the tapioca pearls become predominantly translucent. Regular stirring is required during this period.

In a separate mixing bowl, combine the beaten eggs with the remaining 3/4 cup of granulated sugar.

Gradually introduce the hot milk and tapioca mixture into the egg and sugar combination, adding approximately 1/4 cup at a time. Continue this process until approximately half of the hot mixture has been integrated.

Transfer the tempered egg mixture back into the saucepan with the remaining hot milk and tapioca mixture. Stir the combination thoroughly.

Cook the entire mixture, stirring continuously, for an additional 2 minutes, or until a noticeable thickening is achieved.

Remove the saucepan from the heat source and carefully incorporate the pure vanilla extract.

Transfer the completed pudding to a serving bowl and cover it with plastic wrap to prevent the formation of a skin. Place the covered pudding in a refrigerator to chill before serving.