In a small bowl, combine the baking soda and vinegar. Stir until baking soda is dissolved.
Cream the butter and sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on HIGH until the mixture is fluffy and creamy, about 3 minutes.
Add the egg and mix 1 minute.
Add the baking soda/vinegar and mix well.
In a medium bowl, whisk together flour and salt and add to the creamed butter mixture. Mix on low just until the flour is incorporated.
Transfer the dough to plastic wrap and shape into a disk; chill for 30 minutes.
Heat the oven to 350°F and adjust the oven rack to the middle position. Line 3 large baking sheets with parchment.
After the dough has chilled, place it on a lightly floured work surface and roll to 1/6-inch thickness.
Cut into rounds (I used 1¾-inch fluted rounds), and transfer the cut dough to the prepared baking sheets. The dough spreads very slightly, so leave about 1-inch between rounds.
Bake cookies at 350°F for 11-14 minutes or until golden brown and crisp. (I prefer these cookies extra crispy.)
Transfer cookies to a cooling rack and completely cool before icing.
Melt the chocolate in the microwave on HIGH until melted and creamy. Stir every 15 seconds with a dry, clean rubber spatula.
Place the peppermint candies in a zipper-style plastic bag and crush with a rolling pin.
When the cookies have cooled, spread with melted chocolate and sprinkle with crushed peppermints.
Let the chocolate set before serving and before storing.
Store in an airtight container up to 5 days.