Björn Hilliges wrote:

There's no reliable way, because the number doesn't need to be
stored anywhere on the phone or SIM.  The number is resolved at
the network level.

Having said that, there's a place for it on the SIM.  It's the
first of (usually) 3 possible entries on the "own numbers" SIM
file.  Depending on implementation, the file can be read in
either of two ways: by using the

       AT+CNUM

command, or by switching to the "own numbers" phonebook with

        AT+CPBS="ON"

(that's the letter "O") and then reading off the first entry
with

       AT+CPBR=1

Note however that the number may never have been written to the
SIM by your carrier.  Furthermore, the number can be edited or
deleted on many phones, either directly or via an "AT" command.
Changing the number has no effect on the behaviour (or the
actual number) of the phone.

John