[ejdyksen]

It's not a native feature of FaceTime, but it is a native feature of macOS--specifically iMessage.

Just start an iMessage conversation, then click "ask to share screen" or "invite to share screen" from the Buddies menu.

https://i.imgur.com/vRtuIQM.png

[checker659]

That doesn't work if the other person is, say, on an iPad.