How to create a custom Twig Template for Menu Block
Ok, I think I found the answer.  Kristian Kaa answers it on his blog here:
http://kristiankaa.dk/article/drupal8-region-specific-menu-theme-hook-suggestion

Basically you use 2 preprocess functions like so:

/**
 * Implements hook_preprocess_block().
 */
function mymodule_preprocess_block(&amp;$variables) {
  $variables['content']['#attributes']['block'] =    $variables['attributes']['id'];
}

/**
 * Implements hook_theme_suggestions_HOOK_alter().
 */
function mymodule_theme_suggestions_menu_alter(array &amp;$suggestions, array $variables) {
  // Remove the block and replace dashes with underscores in the block ID to
  // use for the hook name.
  if (isset($variables['attributes']['block'])) {
    $hook = str_replace(array('block-', '-'), array('', '_'),    $variables['attributes']['block']);
    $suggestions[] = $variables['theme_hook_original'] . '__' . $hook;
  }
}


This will add the block ID as a new theme hook suggestion.  Many thanks to Kristian.