[duffmancd]

This doesn't match with my experience. I have a single catchall *@my-domain.com address that will receive anything sent to the domain (without setting up separate accounts ahead of time).

You can also send from any address, but I agree that the UI is a bit hidden. You first choose from the from-address dropdown "*@my-domain.com", and then a new textbox appears where you can type what address to send from. As another commenter pointed out, if you are replying to an email it will automatically fill in the custom from-address, but you can overrule it.