In a medium bowl, whisk together the flour, baking soda, cinnamon, ginger, and allspice with 1/2 teaspoon kosher salt. Set the mixture aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and brown sugar until fluffy, about 2 minutes.
Beat in the molasses then beat in the egg and vanilla extract, scraping down the sides as needed. (The mixture may look separated, which is normal.)
Add the flour mixture in increments and mix just until combined.
Divide the dough in half and roll each piece between two sheets of parchment paper until the dough is 1/4”-thick. Refrigerate the sheets of dough on a baking sheet for a minimum of 2 hours and up to 2 days.
When ready to bake, preheat the oven to 350°F. Line baking sheets with parchment paper.
Use cookie cutters to cut out your preferred shapes and transfer them onto the prepared baking sheets, spacing the cookies at least 2 inches apart. Dough scraps can be gathered and re-rolled between two sheets of parchment paper, refrigerating the dough again if necessary.
Refrigerate the cut-out cookies for 15 minutes (or freeze them for 5 minutes).
Bake the cookies just until they are set, 8 to 11 minutes. Remove them from the oven and let them cool for 5 minutes on the baking sheets before transferring them onto a wire rack to cool completely.
Decorate with icing (optional) then serve.