Ok, an update on this. When I had my car in for the recall fix I asked about this noise again. I was able to get a technical explanation from the service foreman. Here is what he said:
"The wastegate is closed by vacuum and the electronic pressure valves. The vacuum pump takes just a little while to create enough vacuum to fully seal the wastegate as well as the DME delays the full closing of the wastegate on startup to allow the wastegates to rotate, thus cleaning the valve and seat area. The noise is loudest and lasts the longest on a cold start due to the non-expansion of the wastegate components."