Line a large 6-cup muffin tin with plastic wrap.
Slice the pound cake into 12 half-inch slices. Using a small round cookie cutter or a rinsed-out 5-ounce can (such as a tomato paste can), cut 1 circle from six of the slices. Using a rinsed-out 15-ounce can, cut out six slightly larger cake circles from the remaining slices (you should have 6 small circles and 6 large circles).
Set the small circles of cake into the muffin tins. Top each cake cup with a scoop of ice cream and place the larger circles of cake on top to form a lid. Press down on the treat gently to make sure the cup is all filled in and then wrap the whole tin in plastic wrap and place in the freezer for at least an hour to firm up.