I planted broccoli in my community garden last fall, and this spring, as it neared bearing age, it was overrun with aphids. The worst was the largest plant, which tipped over in a winter storm. (It is often the case that a plant with damaged roots becomes most attractive to aphids.) What to do?
I began by crushing as many aphids on leaves as I could find, and washing the leaves with the hose as I went. I looked over the plants carefully, checking the undersides of leaves and in curled over leaves.
When a leaf was heavily infested, I sometimes broke it off and took it away to a green bin (our municipal composting container here in San Francisco). As it began to bear heads, I removed them too, as they were so full of aphids I didn't want to try to get them clean.
I also noted that there were many lady beetles (ladybugs) on my African blue basil plant (a perennial that was coming back from winter), so I assume some of them were eating aphids on the broccoli, though I never saw one there. And, some of the aphids were turning brown and puffy, since they had been parasitized by the miniwasp that preys on aphids.
But after 2 weeks, with the problem not going away, I used a different pest management tactic, the email. I sent an email to a gardener in an adjacent plot to say that there were so many aphids on the Russian kale in that plot that it was certainly inedible, and so many that they were surely flying over to my broccoli in search of more to eat.
I think this tactic turned the tide. The next time I looked, the infested kale was gone (thank you!) and within a week, the infestation of my broccoli was much lower. I still searched and found pockets of aphids on inner leaves, but it was so much better.
Then, in a couple of weeks, presto, clean broccoli heads! I have been enjoying them ever since. I like to steam a few lightly and refirgerate them to cut up and put on a salad!