Display posts where date field matches current month?

You can use the meta_query parameter to display all events for the current month like this:

$start_date = date( 'ym01' );
$end_date = date( 'ymt' );
$meta_query = array(
    'key'       => 'event_date',
    'value'     => array( $start_date, $end_date ),
    'compare'   => 'BETWEEN',
    'type'      => 'NUMERIC'
);
$args = array(
    'post_type'         => 'hh_event',
    'posts_per_page'    => -1,
    'orderby'           => 'meta_value',
    'meta_key'          => 'event_date',
    'order'             => 'ASC',
    'meta_query'        => array( $meta_query )
);
$the_query = new WP_Query( $args );