Preheat oven to 350°F and line a baking sheet with parchment paper.
In a large bowl, cream together butter and powdered erythritol until light and fluffy.
Mix in egg and vanilla extract until smooth.
In another bowl, combine almond flour, coconut flour, baking powder, and salt.
Gradually add dry ingredients to wet, mixing until a soft dough forms.
Roll out the dough between two sheets of parchment paper to about ¼ inch thick.
Cut into shapes with cookie cutters and place on prepared baking sheet.
Bake 8–10 minutes, until edges are slightly golden.
Cool completely before frosting.
For frosting: beat butter, erythritol, and vanilla, adding cream until smooth and spreadable. Frost cooled cookies and decorate as desired.