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Beat butter and brown sugar with an electric mixer on high speed until fluffy, about 5 minutes. Add egg; mix well. Beat in molasses, cinnamon, ginger, allspice, baking soda, and salt. Reduce speed to low, and add flour, 1 cup at a time, mixing until incorporated.
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Divide dough into quarters; shape into disks and wrap in plastic. Chill until firm, about 3 hours.
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Preheat oven to 375 degrees with racks in upper and lower thirds. On a lightly floured work surface, roll out 1 disk of dough to 1/8-inch thickness. Cut out cookies, rolling out any scraps and additional disks as needed until you have about 24 people. Transfer to parchment-lined baking sheets, spacing 1 inch apart. With remaining dough, cut out additional shapes to make clothes, jewelry, and hair as desired. Dress cookies, then chill 20 minutes.
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Bake cookies 2 sheets at a time, 7 minutes; rotate sheets top to bottom and front to back, and continue baking until cookies are firm when touched, 6 to 8 minutes more. Let cool on sheets 5 minutes. Transfer to wire racks; let cool completely. Decorate cookies as desired.