I'm not positive, but I think one has to wait for it to age enough to have pups of its own.

I'm doubtful this can be grown indoors, it needs very strong sun to keep its color (I've only known this to be grown outdoors by Calif. friends, & some NYers who summer it outdoors.

DM -
If you top our your plant it will send out new branches. If you place the tops in new fast draining soil they will root and make a new plant. You will want to do this as once a rosette has bloomed it dies. If you have several branches it is not a problem but a single branched plant like yours is at present would die. Here's the catch: Aeoniums are winter growers/summer dormant. Don't lop off its head in mid-summer. The best time is in spring or fall while temps are mild.

In the words of a trusted friend: "In my experience, when an aeonium rosette is ready to flower, it's going to flower. I've beheaded the large-rosette types, such as 'Cyclops,' and had them bloom as soon as I get them back in the ground. What the beheading WILL do, at least with the thick-stemmed types, is encourage re-sprouting below the cut before it's too late." PatrickFB

They do like alot of light but it is *my understanding* that a true "Zwartkop" (correct spelling) will always stay purple with possibly a little green near the center of the rosette. There is another hybrid (whose name I cant recall) that looks much the same but will revert to green in shade.
HTH -Jo

Here is a link that might be useful: A. arboreum v. atropurpureum *Zwartkop*