Gives a shortcode of [on_this_date] to display posts from this day, in all years from a site.

on_this_date.php

<?php
/*
Plugin Name: On This Date
Plugin URI: https://kungfugrep.com/
Description: Gives a shortcode [on_this_date] to show posts from this day of the month in all years
Version: 0.1
Author: Chris Klosowski
Author URI: https://kungfugrep.com
License: GPLv2 or later
*/
function ck_from_this_date() {
	$args = array(
		'orderby' => 'post_date',
		'order'   => 'DESC',
		'cat'     => <category_id>,
		'date_query' => array(
			array(
				'month' => date('m'),
				'day'   => date('d'),
			),
		),
	);

	$new_query = new WP_Query( $args );

	if ( $new_query->have_posts() ) {
		while ( $new_query->have_posts() ) {
			$new_query->the_post();
			?>
			<?php echo the_date(); ?>
			<div>
				<a href="<?php the_permalink(); ?>"><?php the_title(); ?></a>
			</div>
			<?php
		}
	} else {
		?><div><em>No posts found.</div><?php
	}

	wp_reset_postdata();

}
add_shortcode( 'on_this_date', 'ck_from_this_date' );