I didn't understand what to do with this statement:
RecursiveIteratorIterator::setMaxDepth ([ int $max_depth = -1 ] ) : void
So, after finding the answer, this is how you incorporate it (for anyone else who was stuck for a while like me!):
// define the depth of the tree to which you want to search
// where -1 = show all layers below the parent
// and 1 = show the first layer, etc, etc
$max_depth = -1;
// set the path to the directory
$this_directory
// do the search
$recursive = new RecursiveIteratorIterator(new RecursiveDirectoryIterator($this_directory));
// now adjust the contents to your desired depth
$recursive->setMaxDepth($max_depth);
