Adapted from: Bon Appétit Magazine, 12/2005
Whisk flour, cocoa, and salt in medium bowl to blend. Using electric mixer, beat sugar and butter in large bowl until well blended. Beat in egg and 2 tablespoons milk. Add dry ingredients; mix just until blended.
Refrigerate dough 1 hour or more.*
Preheat oven to 350°F. Line 2 baking sheets with parchment paper.
Scoop out dough by level tablespoonfuls, then roll into smooth balls.
Place dough on prepared baking sheets, spacing about 2 inches apart about 9-12 per baking sheet. Using bottom of small glass, slightly flatten each ball to about 1 1/2 inch round (edges will crack).
Bake until cookies no longer look wet about 9-10 minutes (do not over bake or cookies will become dry). Let cool completely.
Using electric mixer, beat powdered sugar and butter in medium bowl until mixed well.
Add peppermint extract and 1-2 drops food coloring depending on how much color you like in the filling. Beat until blended well.
Spread 2 generous teaspoons filling evenly over flat side of 1 cookie and top with another cookie, flat side down. Repeat with remaining cookies and filling.
Place crushed candy canes on plate. Roll edges of cookie sandwiches in crushed candies (candies will adhere to filling). Cookie sandwiches can be made ahead. Store in single layer in airtight container at room temperature up to 3 days or freeze up to 2 weeks.
Makes about 10-12 small sandwich cookies