Before anything else:

Be really sure that your endpoint to retrieve this information is reasonably secure. (e.g. using SSL and some authentication like a password) Leaking the information which plugins are installed
on a site might offer a point of attack for hackers.

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I am not going to offer you a ready-made solution but outline two different approaches how to tackle this: Push and Pull.
Push means that your sites report their plugins to the dashboard, while pull means your dashboards actively gets this information from your sites.

Also I am only going to show you the WP side of things. How you handle stuff for your dashboard is a completely separate issue and also probably not a good fit for this site.

So here we go:

Push

By using a WP-Cron you can schedule a site to do something in regular intervals. In our case we could for example schedule a task that gets the list of installed plugins and reports them to your dashboard (code hugely simplified):

// Add the action that does the actual reporting
add_action( 'hourly_report', 'report_plugins' );

// Schedule this action hourly
wp_schedule_event( time(), 'hourly', 'hourly_report' );

// This function does the actual work
function report_plugins(){

    //Get plugin data
    $plugins = get_plugins();

    //create the data you want to send using $plugins
    $args = ...

    // Post the data to your dashboard
    wp_remote_post( $dashboard_url, $args );
}

Pull

Another option is to create an AJAX endpoint to actively get the plugin-data from a site. This would roughly go along those lines (again code hugely simplified):

// Add the AJAX handler
add_action( 'wp_ajax_nopriv_plugin_data', 'return_plugin_data' );

function return_plugin_data(){
     //Again I want to emphasize that you need to ensure the user has the right to access this data.

     //Get plugin data
     $plugins = get_plugins();

     //Encode and return the plugin data
     echo json_encode($plugins);
     die();
}

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I hope this helps to get you started, let me know if anything is unclear conceptionally.