Begin by activating the yeast. In a small bowl, dissolve the yeast in warm water along with a teaspoon of sugar. Stir gently to combine and let it sit for a few minutes until the yeast becomes frothy and bubbly.

In a large mixing bowl, combine the hot mashed potatoes, sugar, potato water, and flour. Mix well until all the ingredients are fully incorporated. Then, add the activated yeast mixture to the bowl and stir until everything is evenly distributed.

Cover the bowl with a clean kitchen towel and place it in a warm, draft-free area to rise for several hours. Allow the dough to double in size. This initial rise is essential for developing flavor and texture in the fastnachts.

Once the dough has risen, add the remaining sugar, lukewarm milk, melted butter, beaten eggs, and salt to the bowl. Mix everything together thoroughly until a sticky dough forms. Gradually add sifted flour until the dough comes together and is stiff enough to handle.

Turn the dough out onto a well-floured surface and knead it for about 3 to 5 minutes, or until it becomes smooth and elastic. If the dough is too sticky, incorporate a small amount of extra flour as needed to prevent it from sticking to your hands.

Grease a large bowl with unsalted butter or oil and place the kneaded dough inside. Cover the bowl with a clean kitchen towel and let the dough rise in a warm, draft-free place for about 2 hours, or until it doubles in size again.

After the second rise, divide the dough into thirds. Roll out each portion of dough on a floured surface to a thickness of about 3/4 inch. Using a knife, cut the dough into diamond shapes, which are traditional for fastnachts. Make sure to cut a slit across the top of each fastnacht with a sharp knife.

Place the shaped fastnachts on a baking sheet lined with parchment paper, leaving some space between each one. Cover them loosely with a clean kitchen towel and let them rise again in a warm place until they become springy to the touch and appear puffy.

Once the fastnachts have risen, heat oil in a deep fryer or skillet to 375°F. Carefully drop the risen fastnachts into the hot oil, raised side down, and fry them until they are golden brown on both sides. Alternatively, you can bake them in a preheated oven as rolls.

Once fried or baked, remove the fastnachts from the oil or oven and let them cool slightly on a wire rack. Serve them warm and enjoy the delicious potato fastnachts as a delightful treat!