Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets.
In a large bowl, cream together the white sugar and butter until smooth. Beat in the eggs one at a time, then stir in the sour cream, milk and peppermint extract.
Combine the salt and bakers' ammonia with 2 cups of the flour and blend into the mixture. Gradually add more flour to make a stiff dough. Leave the dough soft for drop cookies or add more flour to make cut-out cookies. Drop dough from heaping spoonfuls onto the prepared cookie sheets.
Bake for 8 to 10 minutes in the preheated oven, or until golden. When cool, ice with a simple confectioners' glaze that has been flavored with peppermint if desired.
