Preheat the oven to 350 degrees F (175 degrees C). Line 4 baking sheets with parchment paper.

Whisk flour, cocoa, espresso, and salt together in a bowl.

Cream butter and sugar together in a large bowl with an electric mixer until pale and fluffy. Add egg and vanilla extract; beat to combine. Add flour mixture and beat on low speed until well combined.

Roll dough into 1-inch balls. Dip the tops of the cookies into the crushed candy canes. Place candy-side up on the prepared baking sheets, about 1 inch apart.

Bake in the preheated oven until firm, 14 to 16 minutes. Transfer to a wire rack to cool.