Do you then hold the clutch lever in whilst pressing the starter button?.
I've always started my cars with the clutch pedal depressed since reading that it gives the starter system an easier time due to not having to turn so much mechanically. Although the newest one is button start rather than key, and won't go without the clutch down anyway.
I always pump the lever several times on bikes before engaging first gear after cold start up as I've found that it goes in with less of a clunk and the rear wheel is less likely to jolt and the bike stall. It's having the same effect as what you describe in your post isn't it, although I've no idea why I don't start them with the lever in as I do with cars!.
I've been having trouble for weeks now starting the bike.
I knew the battery was okay as i'd charged it a while back, plus you could hear that it wasn't struggling, it simply wasn't catching when trying to start.
At work where i park my bike it's on a slight uphill gradient and obviously on the sidestand so leaning to the left, so then i was thinking it might be dirt in the carbs so i'd put the bike on level ground, which did help eventually.
When it did start it would sound very throaty for a few seconds if using the choke, then after a while would sort itself out, but if it started without using the choke then it would sound terrible and then cut out a few times, and then i would try it with the choke and it would run a bit better so i'd let it warm up for a few minutes then all would be okay.
I got a bit bored with all this on Wednesday then reluctantly spoke to my mechanic who went through the motions of things to try, but i knew he was gonna suggest changing the plugs as a starting point and it's exactly what he said.
But i put new Iridium plugs in well under a year ago, and with the low mileage i do i just wasn't convinced it was them, even more so because once the bike was warmed up it pulled like a train in every gear when i gave it a bit of throttle, and also it was well behaved at the lowest speeds in traffic.
So after another browse around the internet about cold starting someone mentioned about changing to thinner oil during winter as thicker oil can get sticky due to very cold weather.
I'm guessing that it was an American/Canadian post as if you start bordering the ends of 10w/40 oil over here then chances are you won't be riding the bike anyway, because you'll either pass out due to the extreme heat or the roads will be covered in ice or snow. So changing the oil wasn't really an option for me.
Reading about the sticky oil though then made me wonder if it was the clutch plates that needed a little jolt?
So on Thursday morning, when it was supposedly -4 deg. i gave the clutch lever a few pumps then with a tiny bit of choke hit the starter button and it started like it was a hot summers day!
Thinking that was just a fluke, and i maybe had an intermittent fault, i did it again after work, where the bike had sat outside all day in the cold, and again started instantly with no signs of any hesitation or throatiness whatsoever.
Then Friday morning and evening it did the same thing again starting brilliantly with no problems at all.
So there you go, something so simple yet extremely effective.
After reading online and chatting to a few mates about this i now know about some cars needing the clutch pedal pressed down to start them, but in my defence with that one.......i've never driven a car.