Preheat oven to 350°. Process first 6 ingredients in a food processor 1 minute or until ginger is finely chopped.
Beat butter at medium speed with a heavy-duty electric stand mixer until creamy. Gradually add both sugars, beating until light and fluffy. Add eggs, 1 at a time, beating just until blended after each addition.
Stir together hot coffee and molasses in a small bowl. Add flour mixture to butter mixture alternately with coffee mixture, beginning and ending with flour mixture. Beat at low speed just until blended after each addition.
Place baking cups in 2 (12-cup) muffin pans, and lightly grease; spoon batter into cups, filling two-thirds full. Sprinkle with Spiced Streusel.
Bake at 350° for 18 to 20 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 5 minutes. Remove from pans to wire racks, and cool completely (about 30 minutes). Top with Spiced Hard Sauce.