I truly doubt any reputable shop will repair that. Looks too close to the sidewall. When I started the rule was that a puncture needed to be at least one inch from bend in the sidewall when the tire was broke down and looking at it from the inside. Many shops now just will not repair if the puncture is in either the inner or outer row of tread.
The gash on the outside is not necessarily what it looks like on the inside. Are you saying a rock punctured all the way through?
I bet you can find some old school garage that is willing to fix it, despite the RMA recommendations from cb_13. Since these are run flats, worst case is the repair fails and you get a slow leak that you can drive on anyway.
There's conflict in the guidance offered by some vehicle manufacturers and tire manufacturers in relation to repairing run-flats. For example, BMW explicitly states in their owner's manual that repairing a tire isn't an option. However, one of the larger builders of run-flat tires, Bridgestone, does have a standardized inspection and repair process for their run-flat tires.
Which is correct? The tire manufacturers defer to the vehicle manufacturers. So in the case of run-flats on a BMW, repair isn't an option. The bottom line is you'll have to check your vehicle's owner's manual or with your vehicle manufacturer.