In a medium bowl, whisk together the flour, cocoa powder, salt, baking powder, and espresso powder. Set aside.

In a stand mixer, cream the butter, brown sugar, and granulated sugar on medium speed until fluffy, about 3 to 4 minutes. Add the egg and vanilla extract, and mix until combined.

On low speed, gradually add the flour mixture until fully incorporated. Form the dough into a disc, wrap it in plastic, and refrigerate for 1 to 2 hours until firm.

Let the chilled dough sit at room temperature for 5 to 10 minutes until pliable but not sticky. Roll the dough on a lightly floured surface to ⅛-inch thickness.

Cut out circles using a 3-inch biscuit cutter. Transfer them to parchment-lined baking sheets, and refrigerate for 30 minutes.

Preheat the oven to 350°F. Bake the cookies for 10 to 12 minutes until the edges are set and the centers are still soft. Cool on the baking sheet for 5 minutes, then transfer to a wire rack.

Once the cookies are cool, freeze them on a parchment-lined baking sheet for 2 to 3 hours or overnight.

Let the ice cream soften slightly, then spread it into a plastic wrap-lined pan in an even layer. Freeze for 4 to 5 hours until firm.

Cut out ice cream circles using the same 3-inch biscuit cutter. Place one ice cream circle between two cookies to form a sandwich.

Wrap each assembled sandwich in plastic wrap and aluminum foil. Freeze for 8 hours or overnight before serving.