Peel potatoes and cut into uniformly sized chunks. Place in a pot and cover with water. Salt the water about 2 tablespoons.
Boil until cooked through and easily pierced with a fork, about 20 minutes.
Drain potatoes well and return to pot. Let any excess water evaporate. Mash with 1 tablespoon of cornstarch, egg and butter.
Flour your hands with cornstarch and flatten about 1/2 cup of mashed potatoes into a disk in the palm of your hand.
Add a heaping tablespoon of ground beef to the center of the disk and bring the edges of the potato up and around the ground beef.
Seal the edges and roll into a smooth ball. Repeat until all the potato has been used up, making sure to coat hands in cornstarch.
Deep fry the balls in hot oil (at about 350°F) for about 5 minutes, turning as needed until they are golden brown all over.
Serve plain or with mayonnaise ketchup mix or mojo de ajo (garlic sauce) for dipping, if desired.