Preheat oven to 350°F. Line 2-3 baking sheets with parchment paper. Set aside.

Cream 1.5 cups butter and brown sugar with a hand mixer or stand mixer on medium speed for 2 minutes. Add egg, vanilla extract, and salt and beat for an additional minute.

Turn the mixer to low and mix in the cocoa, flour, and baking soda, mixing until just combined.

Use a 1 oz cookie scoop and divide the dough in half to scoop equal-sized balls of dough. Roll each ball between palms to form a perfect circle, then place it on a prepared baking sheet and push down slightly, making a slightly flattened disk. You should have 48 scoops of dough.

Bake for 7 minutes, then remove from heat and allow cookies to cool on baking sheets until they reach room temperature.

In another bowl, beat the 1.5 cup butter, powdered sugar, peppermint extract, and milk until light and fluffy, about 2 minutes. Gently fold in the peppermint candy pieces until just combined. Place frosting into a piping bag with a medium tip.

Pipe roughly 1 tablespoon of frosting onto the bottom half of the cookies, then sandwich it with the top half of a cookie.