In a standing mixer with a paddle attachment, cream butter and brown sugar on medium for 2 minutes. Add in the egg, vanilla extract, and salt and beat 1 minute more.
Turn mixer to low and mix in cocoa, flour, and baking soda, mixing until just combined.
Use a 1/2 oz cookie scoop (or use a 1 oz cookie scoop and divide the dough in half) to scoop balls of dough. Roll each ball between palms to form perfect circle, then place on prepared baking sheet and push down slightly, making a slightly flattened disk. You should have between 36-38 scoops of dough.
Bake for 7 minutes, then remove from heat and allow cookies to cool on baking sheets until they reach room temperature.
To make the buttercream, beat the butter, espresso powder, sugar, and milk until light and fluffy, about 2 minutes. Place frosting into a piping bag with a medium tip.
Pipe roughly 1 tablespoon of frosting onto half of the cookies, then sandwich with remaining cookies. Keep refrigerated. Will last up to 5 days in the fridge.