drupal_admin_form_with_custom_button.php

<?php

//use...

class MySettingsForm extends ConfigFormBase {

  public function buildForm(array $form, FormStateInterface $form_state) {
    //The form
    //..

    //The custom button:
      $form['index']['recreate_index'] = array(
        '#type' => 'submit',
        '#value' => t('recreate index'),
        '#submit' => array('::submitRecreateForm'), //This is where the magic happens!
      );
    }
    return parent::buildForm($form, $form_state);
  }


  //This is called on click of the (not submit) button.
  public function submitRecreateForm(array &$form, FormStateInterface $form_state){
    die('apart button submithandler');
  }

  //This is called on click of the submit button.
  public function submitForm(array &$form, FormStateInterface $form_state) {
    die('general submithandler triggered');
    //parent::submitForm($form, $form_state);
  }

}