Boil the potato in salted water until tender, drain and peel off the skin and pass through a ricer while the potato is still warm, cooling completely.
Zest the lemon and squeeze the juice into a small bowl straining out any seeds. You will need 1/2 cup of juice. Scald the milk over low heat, allow the milk to cool slightly until lukewarm, then whisk the yeast into the milk to dissolve the yeast. Allow the mixture to proof for 5 minutes.
Combine the flour and salt in a large bowl. Add the potato to the bowl of flour. In a small bowl whisk together the egg, sugar, lemon juice, lemon zest, and crème fraiche and then add this mixture to the flour and potato mixture along with the warm milk and yeast. By hand form the dough into a ball. Transfer the dough onto a table and knead the dough for about 2 minutes until the dough is smooth and elastic.
Place the dough into a greased bowl turning it once to coat it and cover with plastic wrap. Allow the dough to rise for 2 hours in a warm place or until it doubles in size.
In a counter-top fryer heat the olive oil to 360 degrees. Using your fingers break off 1-inch pieces of dough and roll them into balls. Fry the dough until its golden brown and crispy. Drain the doughnuts on a paper towel and dust with powdered sugar, serve warm.