I mean at every layer in a transformer, the attention mechanism does a massive state transfer between tokens.

In a recurrent transformer, instead of projecting from the latent space to token space after a fixed depth, you take the latent embeddings and then run them again through the transformer. This causes more time to think because there's more mixing. You can run that as many times as you want for more thinking before projecting the embeddings back to word space.

Personally I believe this is similar to how humans think. The brain is a fixed size yet if we think longer we seem to be able to do more than if we just react instantaneously. This is because the brain feeds the results of our musings back into itself for further thought.