OP, my bone stock US spec 390 with about 11,000 km on the clock has a quirk similar to the one you've described in that it occasionally stalls a few seconds after a cold start while idling. This usually happens while I'm waddling backwards out of my garage, and never happens after I've set off. The bike has never failed to restart after stalling.
I have noticed that this stall only occurs if I have the transmission in neutral; if I have the bike in 1st gear and have the clutch pulled in when I'm manuvering out of the garage, it never stalls. I always chalked it up to a combination of cold viscous oil, and the tiny bit of extra drag on the engine from spinning the transmission by leaving it in neutral with the clutch engaged. Maybe try keeping the clutch pulled in for a little bit after a cold start and seeing if if it still stalls? I'm now curious to see how this would effect your issue.