Force Site Icons to Load Using SSL in Admin

I have my wp-admin configured to use SSL using the FORCE_SSL_ADMIN constant in wp-config.php. However I’ve been getting the infamous “mixed content” error throughout all my admin panels.

Upon further inspection, it turns out that the content causing this error are the site icons/favicons being loaded in the admin over http instead of https.

I am using the site icons feature that was added in WordPress 4.3, which is what is adding those site icons into the head on the admin panels over http. Is there a way to force WordPress to load those site icons using https in the admin?

Here is the view-source where the icons are being loaded, with the website URLs edited, starting line 231:

<script type="text/javascript">var _wpColorScheme = {"icons":{"base":"#999","focus":"#00a0d2","current":"#fff"}};</script>
<link rel="icon" href="https://example.com/wp-content/uploads/2014/06/cropped-Logo-Orig-600-JPG1-150x150.jpg" sizes="32x32" />
<link rel="icon" href="https://example.com/wp-content/uploads/2014/06/cropped-Logo-Orig-600-JPG1-300x300.jpg" sizes="192x192" />
<link rel="apple-touch-icon-precomposed" href="https://example.com/wp-content/uploads/2014/06/cropped-Logo-Orig-600-JPG1-300x300.jpg">
<meta name="msapplication-TileImage" content="https://example.com/wp-content/uploads/2014/06/cropped-Logo-Orig-600-JPG1-300x300.jpg">
<style type="text/css" media="print">#wpadminbar { display:none; }</style>