Preheat to 350°F. Line 2 baking sheets with parchment paper.
Whisk flour, cocoa powder, and salt in medium bowl to blend. Using electric mixer, beat butter in large bowl until smooth. Beat in peppermint extract and vanilla extract. Beat in sugar gradually. Add egg and beat until blended. Add dry ingredients and beat just until blended.
Use a cookie scoop to get uniform balls of dough. Place rounds on prepared baking sheets, spacing 1 inch apart. They don’t expand much, so you can fit quite a few on one sheet.
Roll balls to smooth then flatten with a flat bottomed drinking glass dipped in water.
Bake cookies until tops and edges are dry to touch, about 13 minutes. Transfer baking sheets with cookies to racks; cool completely.
Scoot cookies together so they are all lined up and touching. Place a piece of waxed paper under the cooling rack to catch chocolate drips.
Line a jar or drinking glass with a zipper sandwich bag. Melt chocolate in the microwave and stir until smooth.
Add chocolate to bag then remove from jar. Squeeze out all the air and snip a corner of the bag off with scissors.
Use your piping bag to drizzle all the cookies back and forth in one direction, and then repeat in the other direction to get a criss-cross effect. Let chocolate harden. Place cookies in the refrigerator to speed this process.
Remember that softened butter doesn't mean melted. Take your butter from the refrigerator 20 minutes before starting your recipe.
For best results, take your eggs out at the same time as the butter.
I prefer to use a higher quality chocolate like Ghirardelli for the drizzles as it melts better.