UPDATED:
For http email, it would have to be a service of your web-based email provider. Without hacking their system, if it’s not a turn on / turn off feature in their option set, it’s not accomplishable.

Now, with that said, most providers will display – when you expand the header information – at least the smtp of the service used which is helpful for tracing – depending on your purpose of the trace. Who’s the web-based email provider?