Our SENCo (Special Educational Needs Coordinator) pronounces it ass-p-jers.  I know several teachers who refer to "Spectrum children", meaning that they are somewhere on the autism/asperger's spectrum.

You pick one. You will get corrected in either situation.

.  Wikipedia says Mr. Asperger was from Austria. German is Austria's official language. I don't remember enough German from high school to attempt the pronunciation.