In a large bowl, cream butter and brown sugar until light and fluffy. Beat in egg and molasses.
Combine the flour, baking soda, salt, cinnamon and ginger; gradually add to creamed mixture and mix well. (The dough will be very stiff.) Cover and refrigerate for 1-2 hours or until easy to handle.
On a lightly floured surface, roll dough to ⅛ inch thickness; cut into 2¼-inch to 2½-inch circles. Place ½ teaspoon preserves on half of the circles; top with remaining circles. Pinch edges together to seal. Place on greased baking sheets.
Bake at 350° for 10 minutes or until lightly browned. Cool on wire racks.
Combine glaze ingredients and frost cooled cookies.
