In a saucepan over low heat, melt together sugar, shortening and honey. Let cool.
Mix together eggs, vanilla, baking soda and ginger. Gradually add to cooled honey mixture.
Slowly add 4 cups of flour to mixture. Stir until well blended. Drop by teaspoonfuls onto cookie sheets about 2 inches apart. Bake at 350 degrees F (180 degrees C) until golden (about 12-15 minutes).