Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a mixing bowl, beat the butter, brown sugar, and granulated sugar with an electric mixer until creamy.
Add the egg and vanilla extract, mixing until fully combined.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Scoop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them 2 inches apart.
Bake for 8-10 minutes, or until the edges are set but the centers remain soft. Let cool completely.
Once cooled, scoop a generous amount of ice cream onto the bottom of one cookie and top with another cookie, pressing gently to create a sandwich.
Wrap each sandwich in parchment paper and freeze for at least 1 hour before serving.