In a large mixing bowl, cream the butter, white and dark sugars. Beat in the egg, water and vanilla. In a separate bowl, sift together the flour, baking soda, and salt. Blend flour mixture into the butter mixture, and stir well. Wrap dough in waxed paper and chill at least 2 hours.
Preheat oven to 375 degrees F (190 degrees C). Grease cookie sheets. Cover each thin mint with 1 tablespoon of dough. Place on cookie sheet and top with a pecan.
Bake at 375 for 10 to 12 minutes. Let cool slightly on cookie sheet before removing to racks.