Boil the potato, skin on, until a paring knife can easily be inserted (about 45 minutes). Drain the potato and allow it to cool to the touch. Peel the potato and measure out 250 grams with a kitchen scale. Save the remainder for use elsewhere.

Mix the flours and yeast together in a bowl and pour them into a pile on a large work surface. Use your hand to form a hole in the center, making a volcano shape. Use a potato ricer to mash the 250g of potato into the center (you can also mash the potato in a separate bowl with a masher or fork, then add it to the flour). Roughly mix all together by hand.

Hollow out another hole in the center of the mix and add water. Start by adding ¼ cup (60 ml) of water. Knead the water in until it is well-incorporated, then mix in the salt. If the dough is still dry, continue to knead in a little more water at a time until the dough is soft and smooth but not sticky. If you go too far and the dough becomes sticky, simply dust it with a little more bread flour.

When the dough is thoroughly mixed, form it into a ball and cover it with a large bowl. Let it rest for 10 minutes. Remove the bowl, sprinkle the dough with bread flour, knead it a little bit more (it should be much smoother now), then form it into a ball again and place the dough into the bowl. Cover the bowl with plastic wrap and let the dough rise in a warm place for 2 ½ to 3 hours, or until it doubles in size.

After the dough has risen, transfer it onto a work surface generously dusted with semolina flour. With a knife or bench scraper, cut it into 12 to 15 equal portions. Take a piece and roll it under your palms until it forms a short 'rope' about 12 inches (30.5 cm) long. Press the ends together to form a round donut shape and place on a surface dusted with semolina flour. Repeat with the remainder of the dough to form all of the donuts.

Cover the shaped curujicchi with a clean towel and let them rise for an additional 30 to 45 minutes, or until they visibly rise and puff up a bit.

Fill a large, deep pan with 2 ½ to 3 inches (6 to 8 cm) of oil and bring up to a high temperature on the stovetop. Aim for around 355° F (180° C), but if you don’t have a thermometer, just drop a small morsel of dough in to see if it's ready. When the oil bubbles furiously and immediately upon contact, it is hot enough to fry.

Fry the curujicchi one at a time or in batches of 2 to 3, depending on how big your frying pan is. Carefully place each donut into the oil and fry, turning often with forks or tongs, until golden brown on both sides.

Remove from the oil and place on a paper towel to cool slightly. Serve fresh and warm for best results.