Line a 9 x 13-inch (20- by 30-cm) pan with heavy-duty foil. (If possible, use a nondisposable pan, as disposable pans are smaller on the bottom than the top and a straight-edged pan will make it easier for these sandwiches to come out even.)

Lay half the cookies in the pan, arranging them to form six rows of six cookies each.

In a small mixing bowl, combine oil, peanut butter, and confectioners’ sugar until smooth. Stir mixture into ice cream just until marbleized and spoon over cookie squares.

Smooth evenly over cookies and drizzle with chocolate syrup, if desired.

Cover with remaining cookies and freeze until firm, but not frozen solid.

Remove from freezer and cut carefully between the cookies to form sandwiches. Return to freezer until ready to serve.

To coat sandwiches: Pour toppings into bowls. Working with one sandwich at a time, press sides of ice cream sandwich into desired toppings and replace sideways in pan to freeze.