You can root a cutting if you want. Cut the exposed stem back to half an inch or so (use a knife for a clean edge), let it heal for a couple of days in the shade, and poke that part into the soil so it (but not the rosette) is buried. Within a few weeks, there will be a visible change in appearance of the rosette, and that's when you know that it has started elaborating roots. You have about a 100% chance of success doing this with most Aeoniums, if you do it right.
Bear in mind that summer is the season of rest for Aeoniums, which means they will not root well or grow much until the fall. A certain amount of patience is required in this regard. Another thing which will become important in the lower light of fall and early winter is that these plants demand bright light indoors, especially during their period of active growth. Bright light is also important for the growth and good form of the cutting you are interested in rooting. That would mean hours of indoor sun, probably your sunniest windowsill.
