Override image-formatter.html.twig
In your .theme file, add this suggestions alter hook (and flush caches so the new hook definition is picked up):

/**
 * Implements hook_theme_suggestions_HOOK_alter().
 */
function MYTHEME_theme_suggestions_image_formatter_alter(array &amp;$suggestions, array $variables) {
  $entity = $variables['item']-&gt;getEntity();
  $field_name = $variables['item']-&gt;getParent()-&gt;getName();
  $suggestions[] = 'image_formatter__' . $entity-&gt;getEntityTypeId() . '__' . $entity-&gt;bundle() . '__' . $field_name;
}


Then if you look at the twig_debug output, you should see something like:

&lt;!-- THEME DEBUG --&gt;
&lt;!-- THEME HOOK: 'image_formatter' --&gt;
&lt;!-- FILE NAME SUGGESTIONS:
   * image-formatter--node--article--field-image.html.twig
   x image-formatter.html.twig
--&gt;


Once that is done, you can create your template file called image-formatter--node--article--field-image.html.twig in the templates directory of your theme, flush caches again so the template is picked up, and override the template with any changes you'd like.

This should include a caveat that the code hasn't been thoroughly tested :)