I turned the tap fully clockwise, as usual, to turn of the water.
Still, a significant volume of hot water continued to flow.
I removed the tap handles and used some locking pliers to twist the threaded, brass shanks that remain in the wall, but they were both already stuck tight in the "off" position, as far as they could go.
I don't know much about plumbing. The only way I know how to stop it, short of replacing the shower head with a terminating bolt (like a sump plug), is by using the main valve (outside) at the water meter. But that's getting old real quick.
Where is the problem likely to be located; or which component is causing the issue? And how's it fixed?
Okay, so now I've removed the compression valves from the wall and this is what I've got: