In addition another variant on the same theme using HTML::TreeBuilder::XPath together with HTML::Selector::XPath:
#!perl -w
use strict;
my $html = '<html>
--stuff--
<head>
--more stuff--
</head>
<body>
--still more stuff--
<div class="myBody">
--all the stuff I want, which might include div tags, too--
</div>
--yet more stuff--
</body>
</html>';
use HTML::Selector::XPath qw(selector_to_xpath);
use HTML::TreeBuilder::XPath;
my $t = HTML::TreeBuilder::XPath->new_from_content($html);
my $q = selector_to_xpath('div.myBody');
print $_->as_HTML for ($t->findnodes($q));
# <div class="myBody"> --all the stuff I want, which might include div
+ tags, too-- </div>
The same should also be fairly simple using App::scrape, but the API currently does not allow for returning node elements (and the corresponding DOM tree), only plain text.