I don't so much have idle CPU time as a resource, but "use it or lose it power" - my office is off-grid solar, is "obscenely overpaneled" for winter and experimental reasons (I built a small A-frame over there before going big for the house system, and it's wired in), so I have a lot of power that I can potentially generate, if I can find a way to use it.
I have several systems in there now that just do BOINC compute of various forms. If I have surplus power, I run them, if I don't, I don't. I really need to move them outside in the summer, though - I spend a lot of energy on air conditioning to keep the inside cool.
Pick a project you find useful and go! It'll chew as much idle CPU as you let it!
Probably the best way to monetize an idle CPU is to leave it idle, so that it uses less electricity.
If electricity isn't a concern, and you have a lot of CPU power, perhaps you can get into the cloud business. While AWS and Azure have come to dominate the market, there are still smaller providers (usually called "VPS" providers) that are doing well for themselves.
I have several systems in there now that just do BOINC compute of various forms. If I have surplus power, I run them, if I don't, I don't. I really need to move them outside in the summer, though - I spend a lot of energy on air conditioning to keep the inside cool.
Pick a project you find useful and go! It'll chew as much idle CPU as you let it!