Rosti (swiss-style potato cake)

1 3/4 lb Potatoes (see below)
      3 oz butter, lard or bacon fat
  1 1/2 tb Water or milk
 
  This is a favorite dish of German-speaking Switzerland. Besides being
  served as a side dish with meat or fish, it is sometimes eaten on its own,
  for lunch or even breakfast, with milky coffee.
  
  The potatoes should be boiled in their jackets the day before. These should
  be waxy potatoes of the potato-salad kind. The next day, peel them and
  grate them on the coarsest blade of the grater. Heat a large heavy frying
  pan, and let the fat get hot: then put in the potatoes, sprinkle with salt,
  and fry, turning them constantly. When they have soaked up the butter or
  whatever, add more. Now form a "cake" by pushing the potatoes from the
  edges of the pan into the middle and flattening down the top.
  
  Sprinkle with the water or milk, reduce heat, and cover with a lid or
  inverted dish. Shake the covered pan occasionally to keep the potatoes from
  burning, and leave on low heat for at least 15 minutes. The potatoes must
  stick together, but not to the bottom of the pan. When cooked, turn the
  cake out onto a plate, bottom side up, and serve. (Or alternately, brown
  the other side as well.) . Variations: (1) Saute 2 T chopped onions in the
  fat before adding the potatoes. Don't let them brown. Also note that in
  this version, the potatoes will need less fat. (2) Saute 2 - 3 1/2 oz.
  diced bacon before adding potatoes. You won't need any extra salt. (3)
  Sprinkle cooked potatoes with grated cheese before serving, and heat it
  briefly in the oven to melt it.