I try to improve the days of strangers by offering compliments that (hopefully) clearly have no ulterior motive. The two easiest ways I've found to do this are a. Offer the compliment in passing so that it is obvious I'm not asking for anything as a follow-up because I've already walked away and b. Compliment things that took time, effort or courage (like an elaborate hairstyle or colorful makeup).
Metaphorically speaking as a man with a beard, I appreciate men with beards because the man in question is often very pleased with his beard and, in most cases, took time to develop it. Therefore, it's nearly universally a safe thing to compliment. I've never once complimented a beard and not gotten a grin and at least brief conversation as a result. Sometimes I'll even get a brotherly slap on the back.
Maybe OP got a lot of - or even a few - compliments on his beard, regardless of the state of his jaw, and it boosted his ego.
I usually just talk about something very unlikely to sound predatory or sexual. "I like your hair," things like that. Hair is one I bring up frequently also because one can usually tell whether a lot of effort was made; as I mentioned, I think complimenting something that involved effort is more impactful than just random, possibly meaningless things about the person.
For example, I don't usually say anything about clothes (on men or women) unless there's something particularly striking about them; recently I saw a woman wearing a shirt expressing a political opinion that is not popular in this area (but with which I agreed) and complimented her on it because it seemed like it probably took courage to wear. However, I wouldn't comment on someone wearing a plain white tee.
I have learned that I don't necessarily always enunciate properly and therefore should say "I like your shoes" rather than "I like your boots."
As a man with a somewhat shorter full beard, though not thin by any means. I take a decent bit of pride in it cause even in its most dhaggy state it requires a decent bit of maintenance with grooming to keep it from ingrowing and knotting.
So yeah any compliment is appreciated keep up the good work.