two things I can think of:
1. too high oil viscosity
2. weak "check valve" (correct term?) at the oil filter. I've heard it described two ways; one where the check valve is INSIDE the filter and one where the check valve is in the oil filter attachment assembly. Regardless, since the filter is "upside down", oil will tend to flow out when the engine is off without a properly operating check valve holding the filter full of oil so that there is no immediate flow of fully pressurized oil at startup. As pressure rise the flow is restored and the noise disappears.
A tech may be able to give a more accurate answer but, when my 1991 300E did what you described my mechanic told me to switch to MB OEM filters and the problem resolved immediately.
for what it's worth