You don't want to take just 'any' brood frames, and you don't take them all. Only those frames w/ mostly 'drone' brood as mites will be most prevalent in drone brood comb. Just a few frames from each infested colony, depending on size. REMOVING and Freezing these frames overnight 'breaks' the cycle. Returning them the next day will provide nourishment as bees clean up the bodies.
With BIG infestations, it may have to be done several times during a season.
Creating 'artificial' swarms (making splits, NUC's ) or 'allowing' bees to swarm also 'breaks' the cycle and has the added benefit of making increase 'if' that is what you seek. While a colony is queenless or in transition, varroa can't do their thing.
Some Beeks think varroa is such a problem 'because' we spend so much time preventing swarms (maybe allowing our bees to swarm away for a few seasons would help?……)
……but there may be something to it 'only known' by the bees…….just saying