Preheat the oven to 350°F and line two baking sheets with parchment.
Beat the almond flour, powdered erythritol, coconut flour, and baking soda in a mixing bowl.
Add the butter, egg, and vanilla extract and mix until it comes together in a dough.
Gather the dough and sandwich it between two pieces of parchment.
Roll the dough out to ¼-inch thick and cut it out using holiday-themed cookie cutters.
Place the cookies on the baking sheets and bake for 9 to 10 minutes until just browned on the edges – bake them 30 to 60 seconds less for slightly softer cookies.
Let the cookies cool while you prepare the frosting.
To make the frosting, beat the butter, powdered erythritol, almond milk, and vanilla in a stand mixer until smooth – add more almond milk if needed to thin.