Here's a quick and no-cost solution. Mine mooed away like it was milking time in the parlour, usually on very light throttle (the car, not the cow!). Previous posts are correct - it is the egr valve. The main fault is that it is hard-mounted by two studs/nuts (10mm) on the bulkhead underneath the passenger-side dashboard area. This provide a resonant surface of which Stradivarius would have been proud.
There is no real need for it to be fixed in this way. Unless you want to pay for an Audi aftermarket fix (I believe they have some sort of rubber isolation mount/adapter?) then just undo the two nuts and let it hang. It has enough vacuum pipes etc. going to it to self-support. If you're in any doubt you can always cable-tie it to the more secure hoses/cables nearby.
I've done mine and the mooing has gone entirely. When stationary on the driveway, with the bonnet off and door open I can hear a very faint noise - but it's much more like a dog's "ruff" now
!