I don’t think thawing-refreezing is that bad for the broccoli in a bacterial sense, but it’ll ruin the individual cells and leave you with a kind of cold broccoli puree. It brings to mind the problem facing the Larkins in “The Darling Buds Of May”, Series 2, Episode 1 – “Oh! To Be In England”. All attempts to freeze the Larkin’s strawberries result in a delicious but soggy mess, due to the action of the slowly expanding water within the strawberry cells, as alluded to by philconsequence above. Charley solves this with deft use of liquid nitrogen, effectively freezing the strawberries double-quick and not giving the water inside chance to expand. Therein lies your solution. Defrost to cut, then refreeze with liquid nitrogen.