Ingredients

3 cups all-purpose flour, plus more for flattening rounds 

1 teaspoon baking soda 

1/2 teaspoon coarse salt 

2 sticks unsalted butter, room temperature 

1/4 cup packed light-brown sugar 

1 3/4 cups plus 1 1/2 teaspoons granulated sugar 

3 large eggs 

2 teaspoons pure coffee extract, such as Trablit (available at lepicerie.com) 

1 1/2 teaspoons instant-espresso powder 

6 ounces bittersweet chocolate, chopped and melted 

4 cups heavy cream 

1 1/2 cups packed fresh mint leaves 

6 tablespoons confectioners' sugar 

Pinch of coarse salt 

Preparation

Cookies: Preheat oven to 350 degrees. Whisk together flour, baking soda, and salt in a bowl. In another bowl, beat butter on medium-high speed until pale and fluffy, about 1 minute. Add brown sugar and 1 3/4 cups granulated sugar and beat until combined, about 1 minute. Beat in eggs, 1 at a time, then coffee extract. Reduce speed to low; gradually add flour mixture, beating until just combined.

Scoop 1-ounce balls of dough with a 1 5/8-inch ice cream scoop and place 2 inches apart on parchment-lined baking sheets. Flatten each slightly with the bottom of a dry-measure cup dipped in flour. Stir together remaining 1 1/2 teaspoons granulated sugar and espresso powder in a small bowl; sprinkle mixture over rounds.

Bake cookies until golden on edges, about 15 minutes. Let cool completely on a wire rack. Dip flat sides of half of cookies in chocolate (or spread chocolate on cookies). Freeze on a baking sheet, chocolate-side up, until set, 5 to 15 minutes.

Cream: Meanwhile, prepare an ice-water bath. Bring cream and mint to a simmer in a small saucepan, then remove from heat; let cool completely, 30 minutes. Place in ice bath until well chilled. Transfer half of mixture to a food processor with half of confectioners’ sugar and salt; purée until mint is finely chopped and cream is thick enough to scoop (check after 20 seconds). Then pulse just until whipped. Repeat with second batch.

Scoop 1/4 cup whipped cream onto flat side of each coated cookie. Freeze until slightly hardened, 5 to 20 minutes. Lightly press uncoated halves on top, then freeze until semifirm, about 30 minutes, before serving.