The Type of your mail is wrong.
Your first Type must be
Type => 'multipart/mixed'.
my $msg = MIME::Lite->new (
From => "from@example.org",
To => "to@example.org",
Subject => "My subject",
Type => 'multipart/mixed'
);
$msg -> attach (
Type => 'text/html',
Data => "<html><body>hi</body></html>"
);