***

We have some of these in the west of England called holloways--originally tracks for carts and cattle which have been worn far below the level of the fields over the centuries. Are the walls chalk?

The walls are not chalk but loess.
Otherwise it is the same process as with holloways.
In the fifteenth century Kazimierz Dolny was pestered with recurring fires. So eventually authorities ordered people to move their barns and stocks up the hills surrounding the town spreading along some narrow dales. People went up and down for hundreds of years making many deep passages like that.