I have two questions:
What weight oil do you use? If you use too heavy of an oil weight it may take longer for pressure to rise or oil to circulate.

What brand oil filter do you use? I switched from a non-OEM brand once and had the same noise you describe. The MBZ filter spring "shut" when oil pressure drops (when you turn off the motor) to keep the filter filled with oil so pressure and oil supply is available sooner to the motor

I don't know if their related but it was just a thought

Intruder