This dough is used to make Mushroom Pierogi and Potato and Goat Cheese Pierogi.
Place unpeeled potato in a large saucepan, and cover by 2 inches with cold water. Add 1 tablespoon salt, and bring to a boil. Lower heat to medium, and cook until tender, about 40 minutes. Drain, and peel while still hot, holding the potato with a clean kitchen towel. Pass the potato through a food mill fitted with the finest disk or a potato ricer into a large bowl.
Sift flour, potato starch or cornstarch, and remaining salt into the bowl with the potato, and combine with a wooden spoon. In a small bowl, whisk together egg, creme fraiche or sour cream, and butter, and add to the potato mixture. Mix with a wooden spoon until well combined.
Turn dough onto a lightly floured surface, and knead for 5 minutes, until smooth and firm. Let rest, covered, for about 10 minutes. Lightly flour a clean work surface, and roll out the dough to slightly thinner than 1/8 inch. Use a 3 1/2-inch-diameter cookie cutter to cut out circles; set them aside on a parchment-lined baking sheet, and cover them with plastic wrap while preparing the filling.