Pre-heat oven to 350°F and line two cookie sheets with parchment paper.
In a medium size bowl, whisk together the flour, cocoa powder and salt and set aside. Using an electric mixer, in a separate bowl, beat the butter and sugar on medium-high speed until light and fluffy. Add the egg and vanilla and mix to combine. Gradually add the flour mixture and beat to combine.
Roll the dough into 1-inch balls and roll in granulated sugar to coat. Place the balls on prepared pans one inch apart and bake for 5 minutes. Remove the pans from the oven and make an indentation in the center of each cookie with the bottom of a wooden spoon handle. Continue to bake until the cookies are just set but still look moist – about 4 minutes. Let cool.
Make the filling: combine the chocolate chips and butter in a microwave-safe bowl and melt in the microwave – checking and stirring frequently to avoid scorching – until melted and smooth. Stir in the peppermint extract.
Let cool for a few minutes, then pipe the filling into the cooled cookies using a sealed plastic bag with the corner snipped off. Refrigerate the filled cookies for 15 minutes to set the filling. Store tightly sealed at room temperature for up to 3 days.