1. Preheat oven to 350°.
2. To prepare cupcakes, line 12 muffin cups with foil liners.
3. Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Combine flour and next 6 ingredients (through allspice), stirring mixture with a whisk.
4. Combine buttermilk and molasses, stirring with a whisk.
5. Place brown sugar and butter in a large bowl; beat with a mixer at medium speed until well blended (about 1 minute). Add fresh ginger and egg; beat well. Beating at low speed, add flour mixture to butter mixture alternately with molasses mixture, beginning and ending with flour mixture. Beat just until blended. Divide batter evenly among muffin cups.
6. Bake at 350° for 20 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack. Remove from pan.
7. To prepare glaze, combine powdered sugar and juice, stirring until smooth. Drizzle over warm cupcakes.