For the cookies: Preheat the oven to 325 degrees. Line 2 baking sheets with parchment paper or butter the baking sheets.
In a medium bowl, combine the flour, cocoa powder and salt. Set aside.
In a large bowl using an electric mixer on medium speed, beat the butter, sugar, dissolved coffee and vanilla extract until blended and smooth, about 1 minute. Reduce the speed to low and add the flour mixture, mixing until the flour is incorporated and the dough holds together. At first the dough will form fine crumbs; then it will come together in large clumps.
Divide the dough in half and shape each portion into a smooth ball. Place 1 piece of dough between 2 large pieces of wax paper and roll it out to slightly less than 1/4 inch thick. Remove the top piece of wax paper. Using a 2 1/2-inch star cutter, cut out cookies. Slide a thin metal spatula under each cookie to loosen it, and place the cookies about 1 inch apart on the prepared baking sheets.
Bake the cookies, 1 sheet at a time, until the tops feel firm and look dull rather than shiny, about 15 minutes. Cool the cookies on the baking sheet for 5 minutes, then transfer them to a wire rack to cool. Repeat with the second piece of dough, and then press all of the dough scraps together to form a smooth ball. Repeat the rolling and cutting process.
For the icing: Dip a fork in the melted white chocolate and drizzle it randomly and generously over the tops of the cooled cookies. Immediately sprinkle with crushed peppermint candy. The candy will stick to the warm chocolate.
Let the cookies sit until the chocolate is firm. The cookies can be stored between layers of wax paper in a tightly covered container at room temperature for up to 4 days.