In a large bowl, using a handheld electric mixer or the mixing bowl of a stand mixer with the paddle attachment, cream the butter, zest, and sugars together on medium speed until light and fluffy, about 4 minutes, scraping down the sides with a spatula as needed.
Meanwhile, whisk together the flour, baking powder, baking soda, ginger, nutmeg, allspice, and cinnamon in a medium bowl; set aside. In another bowl, whisk together the eggs, molasses, orange juice, and vanilla extract.
When the butter and sugar are integrated, lower the speed of the mixer, add the egg mixture, beating well, scraping down the sides with a spatula as needed, then add the flour mixture in 3 batches, beating until just combined after each addition. The dough will be pretty dense and slightly dry to the touch.
Remove the bowl from the machine. Divide the cookie dough into three portions, then wrap it in plastic wrap, and chill for at least 3 hours or overnight; this step will make it easier to finish rolling out the dough when it has chilled. It will also mean you only have half of the dough getting warm as you roll it. (It’s a long time, I know, but you want your cookie dough to be manageable and to keep its shape when the cookies are baking, and you won’t get that unless you have chilled solid dough).
When ready to bake, preheat the oven to 350 degrees F—line three baking sheets with parchment; set aside. Remove the cookie dough from the refrigerator and let it sit at room temperature for 5 to 10 minutes before rolling. Using a rolling pin, roll out the cookie dough on a lightly floured work surface to a thickness of ¼ inch.
Using your favorite cookie cutters, cut out as many shapes as the dough will allow, and carefully transfer them to the cookie sheets arranging them 1 inch apart. If the dough becomes too soft, return it to the freezer until firm. Save any scraps and keep them cool in the refrigerator before re-rolling.
Bake until centers are puffed up, and edges are crisp, about 10–12 minutes. Allow the cookies to stand on the baking sheet until the cookies are firm enough, about 2 minutes, then transfer the cookies to a wire rack and let them cool to room temperature before decorating. Repeat with any remaining dough.