You have two choice, neither of which is desirable or easy.

1. Collect Brome seeds. Burn the field a few times over the course of a year, and then sow the Brome.

2. Don't let the Bluestem go to seed. Methodically deadhead/pull every plant for at least a few years.

I don't know where you are, but in many parts of the US, both can be invasive, and usually Bluestem will win the war.

I know It sounds completely opposite of what most of the websites mention, because usually all the websites I have seen mentions Big bluestem being invaded by smooth brome (but they never mention it being completely overtaken by smooth brome)

Anyway have you personally seen this same situation? Got me to wondering when you said usually bluestem will win the war.. I didn't think another grass species could compete against smooth brome to THAT degree. Where I'm located Big bluestem Is out of Its native range. Even though I'm In the United states my location Is not a native growing area of Big bluestem, but never the less Its here and competing very well against smooth brome which If In time I was to do nothing It would wipe smooth brome out or almost out.