This is easy to do with Nagios and the check_http plugin, and Nagios is then your dashboard for not just SSL expiration but every other service you are (or should be) monitoring as well.
Simple if you already have Nagios set up and running... far from simple if you haven't.
Though someone here posted a video a couple of years ago where the speaker was imploring "Stop using Nagios [it's terrible]". At the end, someone asked him what they should use instead, to which the speaker didn't have an answer (his tool that he was speaking about was still in development)
Edit: but yes, you're right in that the important thing is that the tool will alert you without you having to remember to check it.
Though someone here posted a video a couple of years ago where the speaker was imploring "Stop using Nagios [it's terrible]". At the end, someone asked him what they should use instead, to which the speaker didn't have an answer (his tool that he was speaking about was still in development)
Edit: but yes, you're right in that the important thing is that the tool will alert you without you having to remember to check it.