In a medium bowl, whisk together the gluten free flour, baking soda, salt, and baking powder.
In a separate bowl, beat together the butter, cream cheese, and sugar. Add the vanilla extract and egg and beat until combined.
Mix in the flour mixture at low speed until dough begins to form.
Separate the dough into two equal balls and press down to flatten the top of each dough disk. Place each in a plastic bag. Chill for at least one hour.
When ready to bake, preheat oven to 375 degrees and line a baking sheet with parchment paper.
Remove one dough disk from the refrigerator. Roll out the dough on a lightly floured surface until the dough is around ¼ inch thick.
Use cookie cutters to cut out shapes and place them on the prepared baking sheet.
Bake the cookies for 8 to 10 minutes, until the cookies are golden brown on the edges.
Repeat, balling up the dough after cutting out shapes and rolling it out again until all the cookies have been made from both portions of dough.
Allow to cool on the pan for five minutes, then transfer them to a wire cooling rack to cool completely.
When the cookies are cool, ice with your favorite icing and serve.