For the cookies (adapted from Hershey's):
1/2 cup unsalted butter, softened
3/4 cup sugar
1 large egg
1 large egg yolk
1 teaspoon vanilla extract
1 1/3 cups all-purpose flour
1/2 cup dark cocoa powder
1 tablespoon ground espresso beans (optional)
1/2 teaspoon baking powder
1/2 teaspoon baking soda
1/2 teaspoon salt
For the buttercream:
6 tablespoons unsalted butter, softened
1/2 to 1 teaspoon peppermint extract
2 cups powdered sugar
2 to 4 tablespoons milk
Beat the butter, sugar, and vanilla in large bowl until light and fluffy. Add the egg and egg yolk and beat for 3 minutes. Add the flour, cocoa, ground espresso beans, baking powder, baking soda, and salt, and beat until there is no more visible flour and a soft, dark dough comes together. Scrape down the sides of the bowl and make sure the dough is fully mixed.
Pat the dough out in a long rectangle, wrap in plastic wrap and chill for at least an hour. (Alternatively, roll between wax paper and chill 30 minutes before cutting out the cookies.)
Heat the oven to 325°F. Line a baking sheet with parchment or a non-stick baking mat.
Unwrap the chilled dough and place onto a large piece of wax paper. Cover with another piece of waxed paper and roll out with a rolling pin to 1/4-inch thick. Remove the top piece of waxed paper and cut out shapes with a sharp cookie cutter. Transfer the cookies onto the baking sheet sheet (I like to use a metal spatula for this). Re-roll scraps as needed, chilling the dough if it seems too soft and is sticking to the paper too much.
Bake the cut cookies for 5 to 8 minutes, depending on their size, or until no indentation remains when touched. Let cool on the baking sheet for 10 minutes to firm up, then transfer to a wire rack. Let cool completely before making sandwiches.
While the cookies cool, make the buttercream. In a large bowl, beat the butter together with 1/2 teaspoon of the peppermint extract until pale. Gradually beat in the powdered sugar, adding splashes of milk as you go until you've incorporated all of the powdered sugar and have a thick, spreadable frosting. Taste the buttercream and add more peppermint extract if needed.
Spread the buttercream onto half of the cookies; the amount you'll need will vary depending on the size of the cookie cutter you used. Top with the remaining cookies and store in an airtight container.