How do I define a template file for a specific node paragraph ID? I would like the ability to override a template for only 1 paragraph.  Is it possible to override just one paragraph like we can with nodes node-{nodeid}.html.twig?
This can be easily achieved by implementing hook_theme_suggestions_HOOK_alter from within a custom module or your theme. After that you can override paragraphs by adding templates like paragraph--123.html.twig to your theme's template directory.

/**
 * Implements hook_theme_suggestions_HOOK_alter().
 */
function MYMODULE/MYTHEME_theme_suggestions_paragraph_alter(array &amp;$suggestions, array $variables) {
  $paragraph_id = $variables['elements']['#paragraph']-&gt;id();
  $suggestions[] = 'paragraph__' . $paragraph_id;
}