Four Valley II bath sink faucet cartridges replaced, all work smooth as silk, what pampering this is!
BUT
The most used left sink HOT cartridge only works that way until the water gets HOT, then it give resistance and rubber-squeak-sounds when turning it off ... the HOTTER the water, the more resistance until afraid to allow water to get too HOT, else not able to turn off & must resort to under cabinet OFF valve which may not turn, since never turned in 10 years.

Cause?
Solution?

Ordered all new parts, save the big brass stuff.
There were some brass residue about after the cartridge changes.

Winner gets an AttaBoy from at least me, if not others.

https://www.amazon.com/dp/B000HEA8SS?psc=1&ref=ppx_yo2ov_dt_b_product_details

Can you post a pic of the cartridge?

Old school valley brass ?

I'm not familiar with those faucets, but I would first check the spindle assembly in the handle. It might be dry (needs silicone lube) and/or new o-rings, or needs replacement altogether.

Good responses and tips, thank you all.

Soaked handle in vinegar when CLR didn't do much quickly to that thick calc.build.up = nothing solved

Assembled all the parts needed, then waited for an expert plumber (A.G.) to return, afraid if I turned any 40yo knobs, I might have to shut off main valve @ street for days, waiting for an appt.

Solution:
New cartridge replaced the new-faulty one installed last week
waterproof silicon plumbers grease
The End

Hope sharing helps others.