In bowl of a standing electric mixer beat together dough, honey or molasses, and spices until just combined well. Halve dough and on sheets of wax paper form each half into a 12-inch log. Chill logs, wrapped in wax paper, at least 2 hours or overnight. Preheat oven to 350°F. With a sharp knife cut logs into generous 1/8-inch slices and arrange 1/2 inch apart on baking sheets. Bake cookies in batches in middle of oven until pale golden, about 12 minutes, and cool on racks. In a small bowl whisk together icing ingredients and transfer to a sealable plastic bag. With scissors cut an 1/8-inch opening in one corner of bag. Arrange cookies as close together as possible on sheets of wax paper and drizzle with icing. Let icing dry completely. Cookies may be stored between layers of wax paper in airtight containers up to 6 weeks frozen.