In a large bowl or the bowl of your stand mixer fitted with the paddle attachment, cream together the butter, brown sugar, and sugar until light and fluffy, about 2 minutes. Beat in the egg white and vanilla and set aside.
In a separate bowl, sift together the flour, cocoa powder, salt, and baking powder. Add the dry ingredients into the creamed butter mixture and stir just until combined. Divide the dough in half and transfer it onto two sheets of plastic wrap. Roll each piece of dough into roughly a 2-inch thick log, wrap in the plastic, and place in the refrigerator for at least 4 hours.
When ready to bake, heat your oven to 350ºF and line two large sheet pans with parchment paper. Retrieve the cookie dough from the fridge and, using a sharp knife, slice into ¼-inch thick disks. Transfer onto the baking sheets, being sure to leave at least 1-inch between each. Bake for 9 to 11 minutes or until the surface is matte then set aside to cool completely.
Using a ¼-cup scoop, scoop the ice cream onto one of the cookies and sandwich with another. Serve immediately or wrap and transfer to the freezer for up to 2 weeks. Alternatively, you can store the unfilled cookies in an air tight container at room temperature for up to 1 week and simply fill with ice cream whenever a craving strikes.
