The best way to prevent an invasion of cabbage loopers is to place row cover over plants as soon as they are put in the ground, and leave the covering on until the harvest is over. The cover will prevent most of the worms and moths from finding the broccoli. Once your harvest is over you should remove all the remains of the plants from the garden to prevent carry over of larvae. The adult stage of the cabbage looper is a gray moth that flies by night. They can be stopped by sticky traps placed among the plants.
The worms travel like inch worms, "looping" their bodies as they crawl over the plants. If you see one, just squish it. They are full of green stuff! :-) Cabbage loopers have many natural enemies, including yellow jackets and various parasitic wasps. Planting companion plants which attract these enemies will help cut down on damage to cabbage and other brassica plants. Nectar producing flowering plants planted with broccoli, such as calendula, english daisies, tansy and yarrow attract many beneficial insects which will parasitize and kill the worms. You may even find a mummified worm which has become parasitized if you look closely.