My North Node is at 26° Libra (12th H), and conjunct Mercury (20° Libra) (12th H). I only met one person with Virgo Moon in 10th H, so it's rare for me ^^
I couldn't find any good article about this placement in english, so I'll do you a synthesis based on my experience and articles I read in my langage
The first thing to know is that Moon is in exile in 10th house. Basic role of the Moon is to care for water things that belongs to 4th house (pure affective life, listen to emotions and feelings/"heart", enjoying family, private life, home, free time, etc). But Moon in 10th house is all about carreer, status, how unknown people see you, reputation, future/destiny.
So moon has to support pure material/structured things (and not just pure emotional life/roots and wellbeing)
Virgo Moon is ruled by Mercury (intellect), so it can make people prone to obsessive thoughts.. mainly about health matters : hypocondria, OCD, nosophobia, or eating disorders (moon rules food), etc..- 10th house represent how you're seen by unknown people, so it can also lead to social anxiety. Or in other cases, extreme fears of failure, extreme perfectionnism, burn outs..
Even if I have a Leo MC, I prefer to be not known and stay hidden. I don't have social media accounts, I don't care for recognition and approval of other people. (even if my work is an artistic one. What I want is just to know that I did a good work, in a concrete objective rational way. And I don't need other people to tell me what I should think about it. Even if they think it's good, It won't make me feel emotionaly secure. I need to feel it myself because I'm a very stubborn person (mars+pluto in 1st). Worsts nightmares of Virgo Moons in 10th house are things like unemployment, big failures, uselessness, lack of money/stability/ressources, unknown future, etc..
I can't really say what are the qualities of Virgo 10th H Moon, because I'm also a Virgo Sun. It's difficult for me to differentiate what belongs to my moon and what belongs to my sun, even if they are in differents house (my Sun is in 11th)
Virgo Moons have virgo traits in general I guess. They are good at improving concrete things, seeking solutions, seeing details, learning or teaching, writing, doing lists, helping people, hardwork, etc..
Moon in 10th house can represent several things, like "working with public"/ having a similar profession than one of your parents / working with women (represented by Moon) / or an important woman in your destiny