I know some of the ingredients but not all, and of course don't know the recipe.
Looks like the surfactant blend is SCI and coco glucoside; it has some oils, stearic acid, coconut acid (which I don't know), panthenol, aloe, glycerin, and sucrose cocoate (which I also don't know but it almost sounds like soap).
So, at the end of the day, it is very much like a fancy syndet shampoo bar. I would experiment either based on a syndet shampoo bar recipe that works for you, or with the surfactants that were used here.
Unfortunately, I don't think a home-made bar is ever going to be as hard as this one, since it would require milling.
As for an update on the bar if anyone ends up finding this: I have been using it for a month now and still quite like it. I use it on my hair as well and although I can comb through it afterwards, I found that a bit of leave-in conditioner really helps; otherwise it ends up very static (but I have really fine hair so that's often a problem). It's a long lasting bar; after a month's use I still have about ⅔ of it.