Go out and pick them off... they're probably caterpillars. You keep picking them, they'll be gone.

Get some BT spray (sold as Thuricide) and a spray bottle.

Mix it according to label instructions and add a tsp of baby shampoo or mild liquid dish detergent such as Dove or Ivory. Make absolutely sure that the dish detergent is NOT anti-bacterial.

Spray your plants with this on the top and undersides of the leaves. Wait 3 days and repeat. Wait 5 days and repeat again. Then spray every 7 days with this solution.

It is completely natural and organic and if you use it, there will be no more caterpillars on your broccoli.

Hand picking, as has been pointed out, is very effective if you choose that route. Personally, I have too many plants and my time is simply too limited to do it that way.

Look for Bacillus thurigiensis - Kurstaki, brand nmase of Thuricide, Dipel, and several others, and mix an spray according to label directions. Do not add soap or detergent to this mixture because the products already have stuff in them to aid sticking to leaves that is much safer to the bacteria than any soap or detergent you would add..
Insecticidal soap, mix 1 teaspoon of soap in 1 quart of water, will also work but with that you need to hit the wee buggers because insecticidal soap is a contact poison.

Adding soap to the mixture will indeed cause the solution to stay on the leaves rather than bead up and run off.

That is the reason I add it.

If one reads the label of the Thuricide bottle it clearly says that mixing other items with the solution is not deleterious to the bacteria.

good_gardening1, when I mix up 1 teaspoon of soap in 1 quart of water and spray that on many insects I see them die pretty quickly. If soap does that to the larger forms of life why would it not do the same thing to bacteria spores. If I wash my hands with soap and water that wil lkill the bacteria on my hands, so why would adding soap to a solution containing bacteria spores do the same thing?

Read the label kimmsr.

Read the label. The label specifically says that adding other substances to the mix is not deleterious to the effectiveness of the BT.

I have been adding a small amount of soap to my BT mix for years. Especially for cole crops which are particularly repellent. Otherwise, I am just wasting my time spraying on a solution which rapidly beads up and rolls off onto the ground.

There has been no reduction in effectiveness when applying it to the plants. The insects are just as dead from consuming it.

As to why soap kills bacteria when you wash your hands, the answer is in concentration.

Larger life forms, such as aphids etc are suffocated by the soap or the soap breaks their coatings and they dehydrate.

Experience is a good teacher. I wouldn't recommend adding soap to BT if I didn't know that it was highly effective in solving the beading up and running off problem.

i don't think soap DOES kill bacteria. it just helps "cut through" oil, to which the dirt is attracted, allowing it to dissolve in water. (oil and water on their own won't, of course, mix.)

there are the antimicrobial soaps now on the market, but they have something added to them (which, btw, i read causes nerve damage. google "antimicrobial soap" for more info.)

Be truly organic and eat it raw. Train yourself to eat the worms. They really don't affect the taste and it is meat with no additives or hormones.

if the worms are slugs, coffee grounds repels them. and it feeds GOOD worms and nourishes the broccoli and the soil.
if you use natural mulch, coffee will cause more rapid breakdown of the mulch so you will need more mulch more often, but you will have a richer soil to show for it.
John

A little soap will not hurt bt spores, I wouldn't think. It will disrupt some microbes. I think the mode of activity on insects is that it screws with respiration- which is very different from how microbes breath.

I use Dipel dust in the powder form- one bag lasts forever, and you have to reapply after a rain anyway

How to use BT: "If sprays (of BT) roll off leaves rather than ahdering to them, add a few drops of liquid dish soap to the spray solution to enhanse sticking." THE ORGANIC GARDENER'S HANDBOOK OF NATURAL INSECT AND DISEASE CONTROL

"Combinations with....spreader-stickers in the tank are generally not deleterious to Thuricide if used promptly." Thuricide bottle: Directions for use

I have done this for many years, especially on the Brassica family(kale, collard, broccoli etc.) with no problem. Just use a quality liquid soap (I like to use Dr. Bronner's) and use as little as possible. Some plants are more sensative to soap burn than others.