To add to Freeman's excellent answer, the important takeaway here is that a slab that is made up of a lot of little oddly dimensioned pieces is a function of most of these being factory made.
One could make this in the home shop, but they'd have to be pretty neat with the never-ending jointing (on all sides!) and careful with glue-up and clamping. I suspect one would have to do this in stages, or have a dedicated clamping setup to handle all the slippy pieces. Not to mention that it is hard to clamp along two axes, so you might need to make a bunch of staves that are then clamped together and trimmed to size.
And, while modern glues are amazingly strong, each of those hundreds of joints would have to be well made or natural wood movement will separate at least one of them over time. This is because factory methods can control glue application, clamping pressure (probably managed with strain gauges) in all directions, heat, and humidity for near-perfect seams. They will have this dialed in for the material and joints in a way that would be hard (but not impossible) for the home shop.
There are techniques for making panels from smaller pieces, of course. But few shops would do it the way Ikea, et al, do. There are also some tricks with respect to slightly hollowing out joints to make sure the seam is nice and tight. (For all I know, the factory methods do this, as well.)
This does not address how the panel will then have to be surfaced. A power planer would work, though the potential for snipe over joints might be problematic. I would not want to hand-plane a door-sized piece, but with the right skill and tools it can be done (obviously). If you have a thicknesser/planer/sander you could glue up panels that fit the maximum dimension of that and then glue up the large panels so only that seam needs to be trued afterwards.
But the takeaway is that the look and construction of these large panels made from hundreds off smaller offcuts is made possible by factories where humans load up machines and help arrange orientation, and robots do the rest. In my opinion there is very little that translates to actual woodworking with hand or power tools when looking at the results. Not to mention that it would be a huge amount of work to do this in the home shop, even with all sorts of power tools, and there is no guarantee one will get the same results as we see in the picture.