Accelerator pedal, if floor all at once, car goes into a "limp mode"

What is your question?

If I floor the pedal, my E500 2003 Mercedes reduces power to a gradual crawl, gradually picking up speed. The car remains in this lack of power mode until I stop, turn car off, then start again. If I initially gradually push the accelerator pedal, then increase the speed of my foot pushing the down, then there is plenty of power. What could cause this?

What makes this problem better or worse?

flooring the pedal