In a large bowl using a handheld or stand mixer fitted with the paddle attachment, beat the contents of the sugar cookie package and butter until the dough resembles coarse crumbs. Add the egg and vanilla extract and beat on medium speed until the dough comes together and forms a ball.
Wrap the dough in plastic wrap. Press down slightly on the dough ball to flatten. Refrigerate the dough for at least 4 hours or overnight. You must chill the dough!
Remove the chilled dough from the refrigerator 15 minutes prior to rolling to allow the dough to soften slightly and become more manageable. Preheat the oven to 350 degrees. F. Line 2 baking sheets with parchment or a silicone baking mat.
Lightly flour your work surface with gluten-free flour. Roll the dough out until it's about an 1/8-inch thick. Using a cookie cutter, cut the dough into shapes. Transfer the shapes to your prepared baking sheets. How many cookies you get out of a batch depends on the size of your cookie cutters and the thickness of your dough. I used a 3-inch round cutter and got 30 cookies out of my batch. Re-roll the leftover dough and continue to cut until all the dough is used. If your dough becomes too soft and difficult to handle, wrap the dough in plastic wrap and refrigerate for a few minutes.
Place the sheet pan with the cut-out dough in your refrigerator or freezer for 10 minutes before baking. This step will help prevent your cookies from spreading.
Bake the cookies for 10-12 minutes, or until the tops and edges are a very light golden color. Allow the cookies to cool on the baking sheet for 5-10 minutes before transferring to a wire rack to cool completely. The cookies must be completely cool before they're frosted.
In a large bowl using a handheld mixer or in the bowl of a stand mixer fitted with the whisk attachment, cream butter and powdered sugar until smooth, about 2-3 minutes.
Add heavy cream and peppermint extract to the bowl. Whip on high until fluffy, about 1-2 minutes.
Frost the cookies however you like. I used a small cake spatula to frost some of my cookies, and I used a pastry bag fitted with a small round tip for the writing. Feel free use sprinkles and peppermint crumbles for decorating.
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