Don't peel them; place the potatoes in a pot of salted water and bring to the boil. Reduce the heat and boil them until fork tender.
Combine the semolina flour, water, and olive oil in a large mixing bowl. Add a pinch of salt. Mix until a dough forms. Transfer it to a clean table and knead it for about 10 minutes to achieve a smooth and elastic consistency. Like any pasta making, add water if the dough seems crumbly. Cover the dough with a damp towel and rest for 30 minutes.
While the dough is resting, prepare the filling. Drain the boiled potatoes and let them cool slightly. Once cool enough to handle, peel the potatoes and mash them in a bowl using the masher or fork. Add the grated Pecorino Sardo cheese, one clove of minced garlic, olive oil, and chopped mint leaves. Season with salt and pepper and mix until well combined.
After the dough has rested, unwrap it and use a rolling pin to roll it out on a well-floured surface until to about 1mm thickness. You can also use a pasta machine if you have one.
Use a round cutter or a glass to cut out circles of dough.
Put a small amount of filling in the center of each round, then fold and pinch the base to seal it on one side. Continue pinching and folding the edges to seal the top of the dumpling, working like you would braid hair, starting on one side and then the other until you reach the opposite side. Place the completed culurgiones on a floured tray as you work. The final culurgiones should be between 2-4 inches in length and between 1-2 inches in width.
It requires some practice, you can also just fold the dough over the filling to create a half-moon shape, then pinch the edges together to seal tightly. Use your fingers or a fork to crimp the edges decoratively.
Bring a large pot of salted water to a boil. Carefully add the culurgiones to the boiling water, working in batches if necessary to avoid overcrowding the pot. Cook for about 3-4 minutes or until they float to the surface and are cooked through.
Remove the culurgiones from the water with a slotted spoon and drain them briefly. If desired, serve hot with your favorite tomato sauce and additional grated Pecorino Sardo cheese. Enjoy your homemade culurgiones!