How to display "My sites" menu in the toolbar for my subsite owners?

I have a main site where new users sign up and create blogs for themselves.

When a user signs in on the main site, the admin toolbar on the top only displays a link to the main site on the left and a Howdy … link on the right.

Every user has his own site and if he signs in on the main site, he would expect to see a “My sites” menu on the toolbar, but it’s not there.

To access the my sites menu, the user has to hover on the “Howdy..”, then click on the Profile link to access his dashboard where he can access links to his sites.

Whereas when he switches to his own subsite, the admin bar there has a “My sites” menu, allowing the user to switch between sites (main site and subsite).

This is very confusing. I would like to have a “My sites” menu on the user’s main site account toolbar as well. Is there a way to do this?

I tried the Custom Admin Bar plugin, but all I could do with it is create static menus which is not a solution in this case.