Leave the ice cream at room temperature for about 15 minutes, until it's soft enough to scoop but not melted. Place 4 cookies, flat sides up, on a cutting board and, using a 2 1/2-inch standard ice cream scoop, put one round scoop of ice cream on each cookie. Place 4 more cookies, flat sides down, on top of each scoop of ice cream and press lightly until the ice cream is at the edge of the cookies.
Put the toffee bits on a small plate and, working quickly, roll the edge of the sandwiches in the toffee bits, using your hand to fill in the spaces with toffee. Place the sandwiches immediately in the freezer and freeze until firm. Wrap well and keep frozen until ready to serve.