I would just cut the affected leaved. It is possible that those leaves were touching the soil or soil got into the leaves by rain or watering. I think it is a good policy to trim off the lower leaves of all the plants to let air movement and prevent soil borne bacterial diseases.

That is black rot. You may also notice a dark subcutaneous (so to speak) layer in what is the equivalent of the cambium in the broccoli's stem. Cutting the leaf will solve nothing.

Kale is very sensitive to it (all types except lacinato), to the point of complete crop failure, broccoli are sensitive, and the plant does not fail but is small and the crop is miserable. collard, cabbage, komatsuna, bekana, lacinato, bok choi, arugula, mustard greens (and reds), and all the root crops in the family (turnip, daikon, hakurei, rutabaga) are less or not at all sensitive to it (cabbage, komatsuna and collard may have a leaf like that, but they will look decent and give you a crop).

Sun, drip irrigation instead of overhead, anything you would do to a tomato basically, they all help. anything that keeps the plants dry, plus high OM and removing all debris after cropping also helps treat the soil. I pull them all, with roots, and bury them in one bed (actually a bed on the other sunnier side of the house), which then gets something else growing. Combine these methods with non brassica rotation, and with luck and one dry summer you may get rid of it.

So, what I've done is pulled all the infected broccoli, roots & all. I notice 3 collard plants with what appeared to be the same markings, only smaller. I trashed the broccoli & replanted the collards out of the garden. Is black rot INSIDE THE PLANT or IN THE SOIL?? If it is the soil... can I replace the soil?? Should I remove ALL of the broccoli?? Thank you so much for helping...

Black rot does not act in the Fall (I believe the cutoff is 45F). It is active in summer, the warmer and wetter the worse it is. It is in the plants and in the soil. I would not pull anything more. It is the same if you pull now or pull in February, since black rot will not be active in the intervening time. Nice garden, by the way. To me that is what a garden should look like.

PS. Black rot is a tropical disease. It originated in West Africa. It loses fights with the local temperate microfauna (hence the suggestion of more OM), but it can survive in bits of brassica (stems for example) that are in the garden and have not composted yet. Just eat all you can, then clean it well in February or whenever you are ready, then add something fast composting, like good grass clippings and shredded leaves well mixed together. I prefer shredded leaves and shredded kitchen scraps, or semi-fresh manure, but I see you are far neater than I am.

As I understand, the BR is just a plant disease. You can consume the vegetable. Don' throw them away. Just trim off the affected leaves.