Whisk the almond flour, cocoa, xanthan gum, salt, and baking soda together in a medium bowl, then reserve the mixture. The dry ingredients should look uniform, without visible pockets of gum or cocoa.

Use an electric mixer to beat the softened butter in a large bowl for 1 minute, then beat in the erythritol for about 8 minutes. A pale, fluffy mixture signals that the creaming stage has developed the needed aeration.

Beat in the egg only until it disappears into the butter mixture. A slightly curdled appearance at this stage is expected.

Set the mixer to low and incorporate the dry mixture in two equal additions, stopping as soon as each addition blends in. The finished dough should have an even chocolate color with no dry streaks.

Enclose the dough in plastic wrap and refrigerate for 1 hour or overnight. Chilled dough feels firmer and is easier to roll without sticking.

Heat the oven to 350°F/180°C and cover a baking tray with parchment paper. The parchment provides a surface from which the delicate baked wafers can release.

Sandwich the chilled dough between two sheets of parchment, roll it out, and cut rounds roughly 2 inches across. A thin, even sheet helps the cookies bake consistently.

Arrange the rounds on the lined tray and freeze them for 15 minutes before baking. The cutouts should feel firm enough to hold their shape.

Bake for 8–12 minutes, using a single test cookie first if possible to judge the baking window. Look for a slight puff and a pronounced chocolate aroma rather than browning, and watch closely toward the end to develop crispness without scorching.

Leave the cookies on the tray for 10 minutes, then carefully move them to a wire rack and let them cool completely. The warm wafers remain fragile, and reaching their full crunch can take a few hours as the erythritol firms.

Once the wafers are crunchy, melt the chocolate with coconut oil in a water bath or microwave, add peppermint extract gradually to taste, and fork-dip each cookie onto parchment to set, using a brief freezer chill if desired. The coating should flow off the fork rather than cling in a heavy mound.

Pack the finished cookies into an airtight container for storage, or freeze them; freeze shaped unbaked cutouts separately if preparing dough ahead and bake those directly from frozen. Let the coating become firm before packing so the cookies retain their clean finish.