Check to see if you're being asked to do something that you know how to do, if so, handle it. If not, let the object you wrapped handle it. I made a small modification: the $self hash reference didn't need to be a reference so I promoted it to a regular hash. Your closure closes over that just fine.

That is, the basic technique is wrapping and delegation. That's it. There's no special magic involved because it's a closure or because %self is a hash or a hash reference. That's probably why you didn't find anything specifically about this, it's a general technique and not something that requires anything new of you.

package YourExtension;
use base 'TheOriginal';

sub new {
    my $class = shift;
    my $extended = $class->SUPER::new( @_ );
    my %self = (
        CELLULAR => undef,
        EMAIL => undef,
    );
    my $closure = sub {
        my $field = shift;
        if ( exists $self{$field} ) {
            if ( @_ ) { $self{$field} = shift }
            return $self{$field};
        }
        else {
            return $extended->$field( @_ );
        }
    };

    bless( $closure, $class );
    return $closure;
}
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