I am not clear why the oil level light would come on after you turn the engine off, but I do know that there is an anti-drainback valve in the oil filter housing, so that the oil does not all run down into the pan when the engine stops. I wonder whether that drain-back valve is functioning correctly?

It is also conceivable that you got a bad oil level sensor when the new one was installed.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue