In a medium bowl stir together the dough and fresh ginger. Working between sheets of parchment paper or waxed paper, roll the dough out to 1/4-inch thickness. Slide onto a cookie sheet and freeze at least 1 hour or chill at least 3 hours.
For topping, combine the flour, sugar, ground ginger, and salt in a small bowl. Cut in butter until mixture just starts to cling together. Cover and chill for at least 1 hour.
Preheat oven to 350 degrees F. Line cookie sheets with parchment paper; set aside.
Peel the paper from the top of the dough. Use a 2-inch round cutter to cut circles from dough (if dough is too firm, let stand a few minutes before cutting). Arrange 1 1/2 inches apart on prepared cookie sheets. Gather scraps, roll, and chill as above. Sprinkle topping over cutouts.
Bake for 14 to 16 minutes or until both the cookies and the crumb mixture are golden. Cool on cookie sheets for 5 minutes. Remove and cool on wire racks.
Vanilla Cookie Dough Base
In a very large mixing bowl beat butter with an electric mixer on medium to high speed 30 seconds. Add sugar and salt; beat on medium speed 3 minutes or until smooth and creamy. Add egg whites and vanilla; beat until combined. Gradually add flour, beating until combined.