Engine sometimes sputters on a hard downshift, what's the problem on 2004 Audi A8 Quattro

while driving at normal highway speed, if I "stomp" hard on the gas pedal the engine will sometimes hesitate or sputter before downshifting, or seemingly lag before firing up to speed

Asked by for the 2004 Audi A8 Quattro
There are about 4000 codes for this engine, so the best thing to do is to have a Pro level tech diagnose this hesitation problem, by scanning the engine/transmission computers while performing a test drive and duplicating the hesitation.