DisplayCarrierExtraContent ajax controller

[prestaciccio]

Hello 
I need help, I'm in trouble. 

I'm using the DisplayCarrierExtraContent hook.
The extra content is a select option. I want to save the value to the DB.

I'm trying to use ajax and controllers. I'm not very experienced and although I'm reading from different forums, I can't figure out exactly how I need to do it.

Into funcion HookDisplayCarrierExtraContent I call  

$display = $this->display(__FILE__, 'giorni_cap.tpl');    

Into the file .tpl I have got:

How should be the Ajax POST to send the selected value to the controller?

I have seen many solutions, but I have not yet reached it alone. 

It should be somethings like this:

And the controller? 

 

I hope someone can help me.

Thanks