How to add a meaningful link in plugin admin panel?

Question

I've read too many times this kind of code to add a link in plugin admin page:

<?php
function plugin_add_settings_link( $links ) {
$settings_link = '<a href="options-general.php?page=plugin_name">' . __( 'Settings' ) . '</a>';
array_push( $links, $settings_link );
return $links;
}
$plugin = plugin_basename( __FILE__ );
add_filter( "plugin_action_links_$plugin", 'plugin_add_settings_link' );
?> 

What this piece of code doesn't answer is my question: how to have the link do what I want it to do.

options-general.php?... or whatever doesn't tell me how from a single link I can trigger a single function in my plugin.

if in my plugin file I have

function my_plugin_function() { ... }

I want the user to be able to click a link <a href="???">Click here</a> so my_plugin_function get fired.

How to do so?

Is there some url formatting which does this trick (something wich may looks like this "plugin-call.php?action=my_plugin_function&nonce=d56f654a465e4&notarealworldexample=donttellmeaboutit")?

EDIT:

Apparently I have to start a bounty to have this question answered.
The question being "How from the admin panel can I have a link trigger a function from my plugin (with an (async)postback ?)?" I think it deserves 5 billions points.
I don't have those and a mere 50 points for such a complex question would feel like a joke.

So here it is "IOU 5.000.000.000 points". The one who answer the question can have it.

Answer 1

Short: You can't. Php functions can't be run "straight" from a button because they run server side. You need either to set a $_POST or $_GET (so you can run the function on the page load) or use ajax/javascript.

You can find multiple answers to this question on the site already. For example this. edit: button/link, doesn't matter.