Ignition Start Crank Key Issue

[DanOx]

So 90% of the time my 318ti won't start on the first key turn. She cranks, but won't turn over. However, 100% of the time she starts on the second key turn - without fail.

I'll put the key in, turn her to run for a second or two. Turn the key too the off position, then turn it to run again & instantly she fires. Is has been going on for a while now.

I have noticed that the very few times she starts on the first try the gas tank is full. Coincidence or some sort of fuel delivery issue? (I have tried giving it a little gas blip while starting but that doesn't have any affect.)

I have replaced the plugs, wires, & coil pack - no change. Everything works great on the car with no other mechanical issues. Just the start trouble.

Not a huge deal, just more of an annoyance than anything else. Any suggestions?