I might collaborate with an old supervisor in the future and would like to keep in touch. Is it a good idea to send an email to him about the progress I've made in my career? Also, what's the best way to approach this? I feel like emailing just to talk about myself is a bit narcissistic -- is it?
I just did that, and I often do. If I'm honest, I don't do that as much as I should. Anyway, unless told otherwise, which, imho, would be rare, that should be acceptable/desirable.
Of course, you won't just talk about your stuff, but ask about his/hers. You do have common interests after all.
Professors are people too! There is no secret in talking to a fellow professional that you know. And, of course, never send a professor a lengthy message.
Be polite, be direct, and informative...
As a supervisor, still being in interaction (on their own initiative sometimes) with former students, MSc & PhDs is one of my greatest pleasures.
Still planning (long after supervision) joint work, collaborative projects with your supervisor should be welcome quite positively. Even for sheer information. Good supervisors, teachers, most of the time, do this job to elevate or guide. They usually are happy when they have succeeded. They are often happily surprised. Apparently, this does not happen so often, and they cannot know. Students forget.
You can cope with narcissism by "sharing" or "returning" your progresses to a person you estimate for what s/he brought to your line of research. Whenever this happens to me (so very rare), I am happy.
I enjoy getting periodic updates from former students. It's nice to think that I've made a positive impact in their lives, and it's nice to hear that they are doing well professionally. And I've sent periodic updates to my advisor every now and then.
As for the best way to approach it, and it not coming off as narcissistic, I'd simply recommend that you keep it brief. Don't delve into lengthy details; professors are busy people! Keep it short and simple. Of course, you can always wrap up with a line like this:
If you're interested, I could give you the particulars. Feel free to get in touch.
Then wish them a good day and include your contact information in your signature block.
Yes, do it. Of all supervisors you've had, there's just this one that you're thinking of reaching out to. That means this supervisor is special. If this is the only supervisor you're caring to follow up with, then that's a compliment.
Also, what's the best way to approach this? I feel like emailing just to talk about myself is a bit narcissistic -- is it?
The best way to avoid making it sound like you're only talking about yourself is to avoid only talking about yourself. Mention someone else, too. For example, the supervisor you're mentioning.
Let them know that one of the topics you really want to bring up, because this topic is quite important, is this: thank you.
Really, ex-supervisors don't get told that nearly enough.