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.

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.