Peel and quarter the potatoes. Boil in salted water until tender. Drain, and put through a ricer. You should have 1 cup.
Stir the potatoes over moderate heat in a heavy-bottomed saucepan for 2 to 3 minutes until they form a light film on the bottom of the pan, indicating most of their moisture has been evaporated.
Beat the flour into the potatoes, then the butter by fractions, then the egg, cheese, and seasonings. Taste for seasoning. Preheat oven to 425 degrees.
With a fluted pastry tube ¼ inch diameter, squeeze the mixture into 2½-inch lengths spaced ½ inch apart onto the baking sheets.
Bake both sheets at a time in preheated oven for about 15 minutes, or until sticks are lightly browned.