Adding Custom Dashboard Widgets

I would like to add a custom dashboard widget that will accept HTML, but I am not seeing a straightforward way to do this. It looks like there used to be a plugin specifically for this called Custom Dashboard Widget Plugin, but it seems that has been replaced by Ultimate Branding, and this functionality is not immediately apparent in that plugin. The closest thing I can find in Ultimate Branding is Admin Message, but I don’t want it to stretch across the whole screen, just to behave like a proper widget. Am I just missing something really obvious here?

I’ve also tried adding a sitewide custom widget in functions.php (creating a child theme first) using code that I lifted straight out of the Codex, just to see if it would work:

/**
* Add a widget to the dashboard.
*
* This function is hooked into the 'wp_dashboard_setup' action below.
*/
function example_add_dashboard_widgets() {

wp_add_dashboard_widget(
'example_dashboard_widget', // Widget slug.
'Example Dashboard Widget', // Title.
'example_dashboard_widget_function' // Display function.
);
}
add_action( 'wp_network_dashboard_setup', 'example_add_dashboard_widgets' );

/**
* Create the function to output the contents of our Dashboard Widget.
*/
function example_dashboard_widget_function() {

// Display whatever it is you want to show.
echo "Hello World, I'm a great Dashboard Widget";

but it doesn’t show up on all sites, just on the main site.

Can you please tell me how to add custom dashboard widgets that will appear in all dashboards? Thanks.