I agree with Kooiker's comments.  As long as you try to mow before the seed head comes out, the downy brome will continue to try to make more seed heads. Allow to let the seed head comes out, and then mow it before the seeds become fully developed.

Also agree with Kooiker that downy brome is a winter annual..... it germinates and gets established in the fall. So, if you want to use a residual herbicide, you want to use it in the fall.