I have used this method for about 3 years. It is an excellent way of raising small numbers of queens. Uses the bees natural instincts, but you get queen cells where you want them. Typically I take a strong hive in early May, take away the queen to make a Nuc. Then I notch cells on 3 frames and mark them. 2 weeks later I take away 2 of the QC frames to make up 2 more Nucs and leave the parent hive with 2 or 3 cells.
If you time the brood cycle break to take place either way before or right after your best honey flows, it works great. If you time it wrong, you sacrifice most of your honey production for the year.
the way a brood break works on varroa: the mites stay on the adult bees during the broodless period. Then when the first brood gets capped, the mites infest those cells at multiple mites/cell. That kills the host larva and the mites starve.
You can greatly increase the efficacy of the brood break if do a mite treatment while the hive is broodless, but some of the treatments are also hard on the queens