For the record, most Aeoniums (especially the ones in cultivation) do branch as adults, some of them sparingly and others with wild abandon.
What's unusual about the plant in the photo is that it was on its way to flowering, but then reversed course and went vegetative instead.
As a general rule it's incredibly easy to get most of them to branch, almost on command actually, by removing the top part of the rosette but leaving several healthy leaves at the bottom still on the mother plant. Basically you remove the top half of the rosette and force the bottom half to branch to survive.
To give you one example I have been growing this variegated Aeonium for years, and my annual cycle (by now ritual) is to behead the plant in the way described above twice, waiting only as long it takes the cutting to sprout new roots and start growing again (maybe 6-8 weeks). Those two beheaded plants will grow up with 8-10 branches each (to be harvested later at my convenience) and the rosette which gets rooted for the second time I will allow to grow full size and flower 1-2 years later. So by judicious use of the knife I can multiply a plant that might branch 2-3 times at most to 20 new heads without losing the joy of seeing the flower.
With a plant like that, no sense in ever running out.