For the cookies:
1 cup all-purpose flour
1/2 cup unsweetened cocoa powder
1/4 teaspoon baking powder
1/4 teaspoon salt
6 tablespoons (3/4 stick) unsalted butter, at room temperature
1/2 cup sugar
1 large egg
3/4 teaspoon vanilla extract
For the chocolate filling:
1/4 cup plus 1 tablespoon heavy cream
6 ounces dark chocolate, chopped
1 teaspoon peppermint extract
Pre-heat the oven to 350ºF. Line two baking sheets with parchment paper and set aside. In a large mixing bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside. In a large mixing bowl with a handheld mixer or the bowl of a stand mixer fitted with a paddle attachment, combine the butter and sugar. Cream on medium speed until pale and fluffy, 3 - 4 minutes. Add the egg and vanilla, scrape the bottom of the bowl, and continue mixing to combine. Turn off the mixer, add all of the dry ingredients, and then turn the mixer on its lowest speed. Mix just until all of the ingredients are combined and form a smooth dough. Scoop out a piece of dough about 1 teaspoon in size and roll it into a ball. Place the ball on the baking sheet and continue with the remaining dough, leaving about 2 inches between each ball (you’ll have to bake the cookies in batches as they won’t all fit in the oven at the same time). Dip the bottom of a small glass in cold water and press the balls flat into discs. Bake the cookies until slightly firm and dry on top, 8 to 10 minutes, rotating the sheets halfway through baking. Cool the cookies completely.
While the cookies are cooling, place a small heavy pot over medium heat with the cream and bring it to a boil. Place the chocolate into a small mixing bowl and pour the boiling cream over it. Gently stir the mixture until the chocolate has melted (if some larger chunks of chocolate have not melted, pulse the bowl in the microwave in 10 second increments, stirring between each interval). Stir in the extract and cool the chocolate filling to room temperature (it should still be spreadable. If the mixture cools so much that it hardens, pulse it in the microwave in 10 second increments, stirring between each interval, until it’s smooth again). To assemble the cookies, arrange half of them upside down on a work surface. Transfer the chocolate to a quart-sized plastic bag and snip a very small tip off from one corner. Pipe about 1/2 teaspoon of the chocolate filling onto each cookie base and sandwich them all closed with the remaining cookies. Store the cookies in an airtight container at room temperature for up to 4 days.