Click to call dialing?

Hopefully a quick question. Does anyone know off any free or paid services that will provide a web-based function to connect 2 regular phones, like Google’s now defunct click to call.

The end result that I’m looking for is to be able to have a link where I can specify my number and the target number, then receive a call from the service w/ the caller id as that of the target, and have it being automatically connected.
Like:
domain.com/?me=5559991234&target=4445551234

Failing the existence or ability to use an existing service, can someone point me to the docs to start setting up my own w/ asterisk?

In Asterisk you can use the Originate method from the Asterisk Managemnet API to do this.