Medium announced Profile Pages on the 27th of November 2020:
Changing your Medium URL, profile picture, bio, display name, pinning a Medium post to the top of your profile, and more!
This gives me a profile page at https://damien-ie.medium.com/. Neat. However, I wondered if I could point a CNAME record to this endpoint, and how it might look using https://blog.damien.ie
I use Cloudflare for DNS, so it was very straightforward (no waiting 24 hours, etc.). Cloudflare offer proxying too, and I tried it with that on and off.
Conclusion
Nope. Not possible. Cloudflare times out. Error 522. The host (medium.com) does not like this request.
Feel free to try it yourself: https://blog.damien.ie
Hopefully Medium will one-day allow this.