Stuck building craftsman style coffee table
You're cutting a mortise.  The classic method is to drill a succession of overlapping holes, using a bit that's approximately the width of your desired mortise.  You then clean it up/square it up with a (SHARP!) wood chisel.

Youtube it and you can see it being done.

I would advise you one small thing:  I wouldn't run a mortise and tenon joint through the middle of a hollow leg.  I'd fill the hollow part with wood, at least at the point that the tenon will penetrate.