In a medium bowl, whisk together gluten-free flour, cornstarch, baking powder, and salt. Set aside.

In another bowl, beat vegan butter and sugar with an electric mixer until creamy, about 3 minutes.

Add dairy-free milk and vanilla extract, mixing until combined.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until a soft dough forms.

Shape dough into a ball, flatten into a disk, wrap, and refrigerate for at least 3 hours.

Preheat oven to 350°F (177°C). Line baking sheets with parchment paper.

Roll chilled dough between two sheets of parchment to ¼-inch thickness.

Cut into shapes and place on prepared baking sheets, spacing cookies about 1 inch apart.

Sprinkle with sanding sugar if desired.

Bake 11–12 minutes for soft cookies or 13 minutes for crisp cookies.

Cool on baking sheet for 1–2 minutes, then transfer to a wire rack to cool completely.

Decorate with icing or buttercream once fully cooled.