Mash potatoes while they are still hot. Add the butter, sugar, beaten eggs, vanilla and salt. Add the potato water. In another bowl, mix 1 cup lukewarm water and 2 tbsp. Yeast and 1 tsp. Sugar. Let rise for several minutes then add to potato mixture. Mix with flour in a large bowl. Knead until the dough is not sticky. Let it rise until the next morning. Roll it out and cut with a doughnut cutter. If you prefer bigger doughnuts, turn a small bowl that has a sharp cutting edge upside down. Let the doughnuts rise until double in size. Fry in deep fat.