<?php
$html = <<<EOD
<p><br/>hello</p>
<p>hello<br/></p>
<p>hello<br/>Chello</p>
<p>hello <i>molly</i><br/></p>
<p>okidoki</p>
EOD;
$doc = new DomDocument;
$doc->loadHTML($html);
$xpath = new DomXPath($doc);
$nodes = $xpath->query('//p[node()[1][self::br] or node()[last()][self::br]]/br');
foreach($nodes as $node) {
$node->parentNode->removeChild($node);
}
var_dump($doc->saveHTML());