Because Château Potatoes or Pommes de Terre Château are sautéed in clarified butter, a waxy potato that will hold together is preferred over a floury or starchy potato (which would be better for baking, soups, roasting, etc.).
The preferred French varieties include Belle de Frontenay, Ratte, Roseval, and Viola. On this side of the Atlantic, La Rouge, La Soda, Red Norland, Red Pontiac, Ruby Crescent, White Rose, and Yellow Finnish all work well. You can also use middle-ground, all-purpose potatoes, such as Superior, Kennebec, Long Island, Canada, Katahdin, Delaware, etc.
The only hard part of producing Château Potatoes is paring them in the classical style to the size and shape of large olives. Once that hurdle has been crossed, sauté them gently in clarified butter, as Escoffier says, "that they may be golden and very soft." Sprinkle them with chopped parsley just before serving.
We have seen another method, where the potatoes (still olive shaped – oh la la) are put in cold water, brought to a boil and kept there for 2 minutes, before being cooled in cold water, dried thoroughly, and then fried in butter – "that they may be golden and very soft." Sprinkle with parsley as before. This method has a few more steps, but allows you to babysit the sauté pan a little less.