If it's not bugs, FWIW, I had possums last season - lost all my broccoli plants, then got some fox urine & haven't seen a sign of them since.....

Here is a link that might be useful: Critter Repellant

Never known opossums to eat leaves, but slugs and cutworms do at night.

The way I deduced possums was:
1.Entire 10-12 inch leaves from multiple plants were disappearing completely overnight; slugs & cutworms leave bits & pieces behind.
2. Found info on the web from other gardeners discussing possums eating their broccoli. Possums are omnivores.
3.Had already observed possums in the yard.
4.Damage ceased after applying the fox urine.

You can search this forum for "possums" to find prior discussions

Last year my broccoli was destroyed and I had no idea what was responsible for the destruction. Then one afternoon I caught the culprit perched on my plant munching away on a leaf. It was a squirrel. They ate the leaves and the emerging heads. The plants were done for and I had to pull them all up. I hate squirrels!

The only way I've had any luck deterring critters like possums, squirrells, and racoons that were causing damage in my garden was to trap and then shoot the offending animal. I did have some luck with spreading amonia soaked rags around the garden but that only lasted until the next heavy rain.

My squirrels don't bother my brocolli. However, they will eat every single strawberry, loquat and peach if I don't exclude them with netting/chicken wire contraptions.