How to check and disable one of the checkboxes in a form?

I found this snippet in the code for a form ($roles is an array of roles).

$form['config_options']['roles'] = [
  '#type' => 'checkboxes',
  '#options' => $roles,
];
// Check and disable the 'authenticated' role.
$form['config_options']['roles'][RoleInterface::AUTHENTICATED_ID] = [
  '#default_value' => TRUE,
  '#disabled' => TRUE,
];

What this does is to check the checkbox for the 'authenticated' role, and then disables it (so it can't be unchecked). This works.

I have a very similar requirement. In a form I have checkboxes for a bunch of fields, where $fields is an array of them. The fields are from user profile. I want to check and disable the 'email' field.

Based upon the code snippet above, I think the solution should be something like this:

$form['config_fields']['fields'] = [
  '#type' => 'checkboxes',
  '#options' => $fields,
];
// Check and disable the 'email' field.
$form['config_fields']['fields'][ -- What to put here? -- ] = [
  '#default_value' => TRUE,
  '#disabled' => TRUE,
];

However, I have no idea what to put in the selector where I've written " -- What to put here? --".

Based upon a comment from Clive I've tried to examine $fields. This is what the devel Default variables-dumper gives me (using short array syntax):

$fields = [
  …
  mail => stdClass Object (
    [__CLASS__] => Drupal\Core\StringTranslation\TranslatableMarkup
    [translatedMarkup:protected] => 
    [options:protected] => []
    [stringTranslation:protected] => 
    [string:protected] => Email
    [arguments:protected] => []
  )
  …
]

So it is a bit more complex than the example given in Clive's comment (e.g. it is an object, not an array (as implied by Clive).

So far I've tried 'Email'.

$form['config_fields']['fields'] = [
  '#type' => 'checkboxes',
  '#options' => $fields,
];
// Check and disable the 'email' field.
$form['config_fields']['fields']['Email'] = [
  '#default_value' => TRUE,
  '#disabled' => TRUE,
];

This does not work.

Help will be appreciated.

Also, if I am barking up the wrong tree, and there exists another way to do this, I shall equally appreciate an alternative solution.

(I am using Drupal 9).