Peel and boil the potatoes until they are soft. Drain and mash them until smooth. Allow to cool slightly.

In a small bowl, mix the warm water, milk, and sugar. Sprinkle the yeast over the top and let it sit for about 5-10 minutes until it becomes frothy.

In a large mixing bowl, combine the mashed potatoes, yeast mixture, flour, egg, and a pinch of salt. Mix until a soft dough forms.

Turn the dough out onto a floured surface and knead for about 5-7 minutes, until smooth and elastic. If the dough is too sticky, add a little more flour as needed.

Place the dough in a lightly greased bowl, cover it with a clean towel, and let it rise in a warm place for about 1 hour, or until it has doubled in size.

Punch down the risen dough and turn it out onto a floured surface. Divide the dough into small balls (about the size of a golf ball).

Flatten each ball slightly and place a small amount of shredded mozzarella in the center. Pinch the edges together to seal the cheese inside, and roll the dough back into a ball.

Heat vegetable oil in a deep frying pan over medium heat. The oil should be about 1-2 inches deep.

Fry the dough balls in batches, turning them occasionally, until they are golden brown and cooked through (about 3-5 minutes per batch).

Remove the dough balls from the oil and place them on a paper towel-lined plate to drain excess oil.

Serve the potato and cheese dough balls warm. They are perfect as a snack or appetizer.