To do that, they need to establish their own call to your destination number and then connect you to it (ie: transfer you through their phone switch). That's the purpose of their callback to you. The carrier of their outgoing line then needs to allow the CPE (customer premises equipment) to transmit its own caller id information, which requires a "Megalink T1" service, which is a T1 with 23 B (bearer) channels and a "D" (data) channel that carries the caller id and other supervisory communications.
I don't see how you could do this with an asterisk pbx unless you have the same digital data channel to provide the caller id (and a central office that allows you to send your own). Unless you're an established business that will use it properly with a large pbx, this is generally not available. You can get Microlink service with two 56k B cannels and a 16k D channel so the technology is possible with a small link to the central office, but I doubt that a carrier would allow you to do this. Like jrfuda mentioned, a regulatory agency would not normally allow just anything to be sent, since that would undermine the whole value of the caller id service offering.
