That's called the stopper. The accelerator plunger is in the big hole.
I had a heck of a time removing one also. I used compressed air. I had to block off the main jet holes and power jet hole to build enough pressure. I used m5 screws for the main jet holes and a m6 screw with a small allen head in the power jet hole. I used a rubber tipped air nozzle to pressurize the stopper passage via the tiny brass orafice. You'll need to plug the big accelerator pump chamber. I also blew air the opposite direction, insert air nozzle in Acc Pump chamber. Wrap something around your air nozzle(chunk of bicycle tube) to create a seal and hold your finger over the small brass tube that delivers fuel from stopper chamber. You could also CAREFULLY heat the stopper and add drops of oil afterwards.
The other thing I've seen done to remove a stopper is drill the center to spin it and thus break it free. I'd avoid this if possible. Stoppers aren't easy come by.
Far right is an OEM stopper that was drilled. It was still usable. Left is one I made from a rivet for a carb that had a missing stopper.
View attachment 1474464