Z4 03 bmw Z4 engine rpm roar up and down around when start up!

I have a 03 bmw Z4, the problem is when I left it overnight. I have the tendency to put my foot on the brake before turn on the ignition. With that, when the engine started, the rpm roar up and down around 1500 rpm to 1000 rpm. And the car shake around 30 second to 1 minutes, after that it's ran normal. I can avoid the roaring, shaking of the engine by avoid pressing the brake when starting. I don't really know what the cause of this issue therefore i'm posting this thread.

All the experts, if you know what's the issue please feel free to post a comment. I'll deeply appreciate your help! thank you!