I would like to shape this thing from 2001 A Space Odyssey, it's a connector to pressurize the suit

I began to add a cylinder, inset the top face, extrude it but now I don't know how to bevel it to make it rounder like in the picture above

Sorry I couldn't find a better quality pic from this connector in the movie.

EDIT : here's a gif of my issue, I followed Sander's instructions but it results in that :

Thank you for your help :)