Okay, I’ve read several of these posts, and found the same thing lacking in them all. A complete misunderstanding of what the people mean.
The blavatar, is on the LEFT site of the admin bar, and is not related to changing the favicon.
Multisites also use it, in front of each site name in the admin bar.
There’s css and code for this:
CSS
#wpadminbar .quicklinks li .blavatar {
float: left;
font: normal 16px/1 'dashicons' !important;
speak: none;
-webkit-font-smoothing: antialiased;
-moz-osx-font-smoothing: grayscale;
color: #eee;
}
#wpadminbar .quicklinks li a:hover .blavatar {
color: #45bbe6;
}
#wpadminbar .quicklinks li .blavatar:before {
content: '\f120';
height: 16px;
width: 16px;
display: inline-block;
margin: 6px 8px 0 -2px;
}
CODE
$blavatar = '<div class="blavatar"></div>';
$blogname = $blog->blogname;
if ( ! $blogname ) {
$blogname = preg_replace( '#^(https?://)?(www.)?#', '', get_home_url() );
}
$menu_id = 'blog-' . $blog->userblog_id;
$wp_admin_bar->add_menu( array(
'parent' => 'my-sites-list',
'id' => $menu_id,
'title' => $blavatar . $blogname,
'href' => admin_url(),
) );