Preheat oven to 350°F. Line 3 cookie sheets with parchment paper.
In a large bowl, whisk together gluten-free flour, cinnamon, ginger, allspice, baking soda, and salt. Set aside.
Combine sugar and butter in a large mixing bowl with an electric mixer; add molasses, egg, and vanilla. Scrape the sides of the bowl as needed.
Add flour mixture slowly to the sugar mixture, until a thick dough forms. Divide dough into four parts and wrap each with plastic wrap. Allow the dough to rest in the refrigerator for 30 minutes.
On a lightly floured surface, roll out one portion of dough to 1/4-inch thickness. Cut out shapes with cookie cutters and place on a baking sheet, 1-inch apart. Repeat the process with the rest of the dough.
Bake 10-12 minutes, depending on the size of the cookies, until slightly golden brown around the edges. Cool completely before removing cookies from pan.
Decorate the cookies as desired with royal icing.