I'm not sure that I'm understanding you. You need your database connection, but don't want to pass is as a parameter all over the place. That is usually done with a factory object. That factory object is a singleton (aka - global) and you ask it for a DB connection. It returns the same MyApp::DBConnection object to everyone. Your code snippet becomes

my $self = shift;
my $connection = MyApp::ConnectionFactory->connection();
my $user = MyApp::DB::User->new({dbh => $connection->dbh()});
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Is this even close to what you want?

Also, that { dbh => $value } thing is ugly. Use BUILDARGS so that the constructor (aka 'new') takes a single arg.

sub BUILDARGS {
   my ($class, $dbh) = @_;
   { dbh => $dbh };
}
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I think that is much easier on the eyes. And instead of creating all the connections at startup time, I'd make 'em lazy and only have them done when necessary.

Good luck.

- doug