Designing a plugin that uses an iFrame to process data in admin

You could target admin-post.php to do the processing via the admin_post_$youraction hook:

This hook allows you to create custom handlers for your own custom GET and POST requests. The admin_post_ hook follows the format “admin_post_$youraction”, where $youraction is your GET or POST request’s ‘action’ parameter.

You can output the URL via admin_url( 'admin-post.php?action=add_foobar' ). Then hook your code:

add_action( 'admin_post_add_foobar', 'prefix_admin_add_foobar' );

function prefix_admin_add_foobar() {
    // Handle request then generate response using echo or leaving PHP and using HTML
}

If you want to update things as you go, then probably AJAX is what you want, which works similarly to the above, with an action parameter that maps to an action hook.