1. In a small saucepan, bring heavy cream to a simmer. Pour over milk chocolate in a bowl; stir until smooth. Press plastic wrap directly onto surface; refrigerate at least 4 hours or up to overnight.

2. Meanwhile, whisk together flour, espresso, and salt in a bowl. In the bowl of an electric mixer fitted with the paddle attachment, beat butter and sugar on medium-high speed until pale and fluffy. Mix in vanilla. Add flour mixture; mix on medium-low until dough comes together. Turn out dough onto a sheet of plastic wrap, shape into a disk and tightly wrap in plastic. Refrigerate 30 minutes.

3. Preheat oven to 350 degrees. Let dough stand at room temperature 10 minutes. Roll out between sheets of parchment until 1/8 inch thick. Using a 2-inch cookie cutter, cut out rounds; transfer to parchment-lined baking sheets about 1/2 inch apart. Reroll scraps to cut out more cookies. Freeze 10 minutes.

4. Bake until set but not browned, about 9 minutes. Let cool on sheets 5 minutes. Transfer to wire racks to cool completely.

5. Meanwhile, whisk the chilled heavy cream mixture until soft peaks form. Transfer to a pastry bag fitted with a 1/4-inch plain round tip. Pipe about 2 teaspoons on bottoms of half the cookies; sandwich with remaining cookies. Drizzle melted dark chocolate over cookies in a crosshatch pattern, if desired. Cookies can be refrigerated in a single layer in an airtight container up to 1 day.