I am wondering if this blog post from Playin with my Food might steer you in the right direction? Apparently these are hugely known in Cleveland as coconut bars, and in Australia as Lamingtons. There are step by step pictures and a recipe by David Lebovitz.

Here is a link that might be useful: Coconut bars or Lamingtons?

Size and shape sure sound like a Lamington. I made these many years ago and they were delicious, if a bit messy to eat. You should be able to Google any number of recipes.

Teresa

coconut cake bars

These are chewy moist coconut bars. This was a special treat during the 1930s and 40s which my mother served often to our farming community by popular demand.

Here is a link that might be useful: cook for book