In a bowl, combine the flour, baking powder, ginger, cinnamon, allspice, and salt. Whisk them together and set aside.
In a separate large bowl, cream the softened butter with the brown sugar on medium speed until it becomes light and fluffy. Incorporate the molasses, followed by the egg and vanilla, mixing until everything is well blended.
Gradually mix the dry ingredients into the wet mixture in two parts, stirring until a thick, cohesive dough forms.
Shape the dough into two discs, wrap each tightly in plastic, and chill them for at least 2 hours or overnight for better flavor.
Preheat your oven to 350°F (177°C) and line baking sheets with parchment paper.
On a floured surface, roll out one disc of dough to about 1/4 inch thick. Cut out shapes with cookie cutters and place them on the prepared baking sheets, spacing them out evenly.
Bake the cookies for roughly 10–12 minutes, until the edges are firm and the centers remain slightly soft. After baking, allow them to cool on the sheet for a few minutes before transferring to a wire rack to cool completely.
For the icing, whisk the confectioners' sugar with vanilla, one tablespoon of milk, and corn syrup (if using) until smooth. Add milk gradually until it reaches a desired piping consistency. Decorate the cooled cookies and allow the icing to set.