The only thing I can say is welcome to the world of emission compliance engines. It will only get worse from here. It is due to the lean mixture that the newer engines run on nowadays, and it is too lean to run correctly when cold.
I have worked on several that start and run that way until they warm up, not only your engine either. Others seem to start and run smooth within a few seconds after starting.
I am wondering what the long term life expectancy of the newer engines will be, because of the lean mix the engine runs hotter.