Pre-heat oven to 350 degrees. Blend flour, ginger, cinnamon, baking soda, and salt in a bowl and set aside.
Cream butter and 1 cup sugar. When well mixed beat in egg and molasses.
When blended stir in dry mixture 1/3 at a time.
Place 1/2 cup sugar in a shallow bowl.
Roll dough into small balls and then dredge in the bowl of sugar.
Place on greased cookie sheet. Bake for 11-13 minutes, until tops are cracked and bottoms are golden brown. They will be soft when removed from the oven but harden as they cool. Place on rack to cool.
When cookies are fully cooled scoop one spoonful of ice cream on half of the cookies and cover with another cookie. Let freeze on cookie sheet for about an hour before placing in a ziploc bag. Will keep for about a week.