In a medium bowl, whisk together flour, baking soda and salt.
In the bowl of stand mixer fitted with a paddle attachment, cream butter and sugar together until light and fluffy.
Beat in egg, vanilla extract and almond extract, scraping down bowl as needed. Slowly mix in dry ingredients until just combined.
Divide dough in half. Place one piece of dough between two pieces of lightly floured parchment paper and roll out to ¼-inch thick slab. Repeat with remaining dough. Transfer both slabs to a baking sheet and chill at least 1 hour or overnight.
Preheat oven to 350°F. Line a large baking sheet with parchment paper; set aside.
Cut out cookies with a 2-inch square cookie cutter, re-rolling scraps as needed. Arrange 2-inches apart on prepared baking sheet, storing unbaked cookies in the refrigerator until needed.
Bake for 10-12 minutes, or until lightly browned on edges. Let cool 3-5 minutes on the baking sheet, then carefully transfer to a cooling rack to cool completely. Continue baking cookies until all of the dough has been used.
Melt half the chocolate in a heatproof bowl set over simmering water. Stir in remaining chocolate and remove from the heat. Let sit a few minutes, then stir until smooth and completely melted.
Dip each cookie halfway into chocolate, letting excess drip off, and return to baking sheet. Sprinkle chocolate with remaining crushed peppermint and let stand until chocolate is set, about 1 hour.