Combine the butter, coconut oil, allulose, monk fruit and erythritol sweetener, liquid monkfruit extract, egg, and vanilla in a mixing bowl. Mix on medium speed until well combined and fluffy. (I recommend using a stand mixer, but a hand mixer or a few minutes beating by hand works, too).
Add the almond flour, coconut flour, salt, and xantham gum. Mix until well combined.
Cover the mixing bowl with the dough in it with plastic wrap and place it in the freezer for about 10 minutes. Meanwhile, preheat the oven to 350°F.
Take the dough out of the freezer and place it between two sheets of parchment paper. Roll the dough out to about 1/4-inch thickness.
Place the rolled dough (still between the parchment paper sheets) on a baking sheet or cutting board, and pop it in the freezer for 5 minutes. Meanwhile, prepare another baking sheet with parchment paper.
After the dough has chilled, remove it from the freezer and use your cookie cutters to make your desired shapes. Place the cutout cookies on the parchment-lined baking sheet.
Place the baking sheet with your cutout cookies in the oven and bake until the edges start to turn golden brown, about 7-9 minutes.
Remove from the oven and let the cookies rest on the baking sheet for 2-5 minutes. Then transfer them to a wire rack to cool completely, which takes about 20-30 minutes.