How to remove rest of Delta Monitor 1500 shower handle?
Have you tried one of these?



These are used for removing pulleys from shafts.  You are likely going to need to sharpen the points to fit.  With a 3 jaw puller it's often useful to wrap a stretchy cord around the jaws to keep them from slipping off a narrow edge.  The end is either a 1/2" or 9/16 end.  use a socket on it.