Line 2 baking sheets with parchment and preheat the oven to 350 degrees F (180 degrees C).
Add flour, baking powder, baking soda, salt, and xanthan gum to a mixing bowl. Whisk everything together until combined.
In another bowl, beat together vegan butter and sugar until smooth and creamy.
Add the flax egg and vanilla extract and mix through.
Sift in the flour mixture and fold everything together.
Roll the cookie dough into balls and dip each in the bowl of sugar to coat it.
Put the dough balls on the lined baking sheets, and bake for 10 to 12 minutes until the edges are set but the center is still soft.
Leave the cookies on the baking sheets for about 10 minutes before carefully transferring them to a wire rack to cool completely. They will be very soft when fresh out the oven but firm up a little once cool.
To Make Vegan Frosting:
Beat butter and vanilla extract with an electric hand mixer until smooth and creamy.
Gradually sieve in the powdered sugar a little at a time, whisking after each addition until incorporated.
Once all of the powdered sugar has been added and the mixture is smooth and fluffy, add the pink food coloring a few drops at a time until your desired color is reached.
Pipe or spread frosting onto each cookie and finish with a few rainbow sprinkles.
Video
Notes
Let cookies cool completely before frosting. Warm cookies will melt the frosting.
Store in an airtight container in a single layer, or place parchment paper between layers if needed.
Vegan Sugar Cookies will last at least 5 days at room temperature.