This follows the sun like a sunflower. I'm thinking I can cut the three stalks and root them and I think the base well produce new branches. I'm clueless.

Yes, Aeoniums can be cut back and will reroot. Here's a YouTube video about such.
https://www.youtube.com/watch?...

I'm not sure if the base will produce new shoots, but I would think so. Looks like it did at one point.

Hi Steve if you leave some stalk on the potted part of stem it'll begin to grow from the stems. And yes the tops can be planted as well
Nice video Tim

Great video, thanks. Should I cut all three stems or do one at a time then when I see new groth cut another. Probably way over thinking this.

Personally I would cut all 3. I usually leave a few inches of the stem for the new growth to develop onto. And I leave a very short stem under the tops which I plant after a day or so of drying off...to avoid rot.

Steve, I think your temps are cooler than my area, so you can certainly cut it. I usually wait to do cuttings in Fall when temps are cooler. In my area, they go semi-dormant when our temps soar, so I wait it out. I also notice it tends to bend like that when it has been too dry for awhile, it gets thirsty, so I give it just a tad more water. We don't have rain here from April to Oct so it really gets so bone dry here.

It will form new leaves/rosettes at the tip. Callus the part you have cut before sticking it to your soil.

Great photos Tarev.