Chocolate Sandwich Cookies with Peppermint Frosting

For the cookies, whisk together flour, cocoa and salt in a large bowl; set aside.

In a second large bowl, beat sugar and egg together with an electric mixer until pale and thickened, about 2 minutes; beat in vanilla.

Add butter and beat again until smooth, about 1 minute more.

Add flour mixture in two parts and beat until combined.

Shape dough into two logs then wrap each snugly in parchment paper, twisting the ends in opposite directions like a piece of candy to tighten each roll and make it uniformly round and about 8 inches long. Chill for 2 hours.

Preheat the oven to 350°F. Line two large baking sheets with parchment paper.

Cut dough crosswise into 1/4-inch-thick slices and transfer to prepared baking sheets, arranging cookies about 1 inch apart.

Bake until puffed and just cooked through, 9 to 10 minutes. Set aside to let cool completely.

For the frosting, put confectioners' sugar, milk, butter, peppermint flavoring and salt into a large bowl and beat with an electric mixer for 1 minute.

Spread the flat side of half of the cookies with some of the frosting, then sandwich with remaining cookies. Serve immediately or store cookies in an airtight container until ready to serve.