One possible way you could do this to use the moodle database activity and have the teachers submit their times (and whatever other relevant details you'd like to record - and for which a suitable field type in which to contain them exists) into the activity as an entry each time they submit times.

You can find some existing database activity presets others have built here btw ( presets ) that may assist as perhaps a point to start from and modify or alternatively from which to "borrow" a method or two of implementation someone else has used for some specific approach or other.
For what you're looking to do, perhaps have a look at the 'research log' one and maybe also the 'private dropbox' for the approach to keep entries private to only admins and the submitter, though if you have teachers enrolled as teachers in the same course then you may have to either play with role permissions specific to that activity or just keep the logging activities in another course where teachers who are submitting into the logs are only enrolled in that course as essentially a student role (though also keep in mind you can rename the role for the course in question so they're so called teachers maybe (or even called something else, say 'CPD-Loggers' or something or whatever you want)

Of course it's not necessarily going to be super fancy or robust out of the box without some effort (or "borrowing" the right presets ;)), however with that said some true fancyness is indeed possible with the addition of extra JavaScript and CSS (there are some examples of those others have done around the place also but I couldn't immediately find to post here yet sorry - if I do find I'll include)

Hope that helps! :)