That shoe needs a new leather sole.
The shoe is "Goodyear welted" where the upper leathers are stitched to the leather sole via a welt. What you see there is the cork filling behind the sole as the sole has completely worn through.
If you send the shoe to the Church's factory (Northampton, UK) they can replace the sole by using exactly the same last (wooden form) that the shoe was made on. This keep exactly the same shape as before. Alternatively, you could send it to a local cobbler where they could replace the sole on a generic last meaning the shape may change slightly.
Ballpark cost for a full resole at Church's would be around £90 GBP I would guess. Local cobbler would be cheaper.
EDIT: This video from a different Northamptonshire shoe maker shows their resoling process.