Put the chocolate and the oil or shortening in a deep saucepan that is not too wide (you'll be using this to dip the ice cream sandwiches, so think about that when you choose your pot). Over the lowest heat, melt the chocolate, stirring constantly to incorporate the oil and make sure the chocolate doesn't burn. As soon as it is smooth, remove the chocolate from the heat and set aside, letting it slowly come to room temperature.

In the meantime, soften the ice cream for a few minutes outside of the freezer. Sandwich about 1/2 cup of ice cream between two cookies, pressing firmly and smoothing the sides. Repeat with the remaining cookies and then return the sandwiches to the freezer for at least half and hour to harden.