Drupal commerce: How to retrieve VAT number from order ID?
It took me a while to figure it out, but now I've found an answer myself:

$profile_id = $order-&gt;content['commerce_customer_eu_vat_rc']['#items'][0]['profile_id'];
$profile_wrapper = commerce_customer_profile_load($profile_id);
$vat_id = $profile_wrapper-&gt;commerce_vat_number['und'][0]['value'];