Those „eggs” are not eggs, but cabbage aphids at different stages of maturity. They feed exclusively on brassicaceae, so other non-brassica plants nearby remain safe.
In dry summers they can cause severe damage and multiply very quickly. Like all aphids they suck the plants’ sap and when the infestation is severe, cause the leaves to shrivel and prevent formation of proper heads.
If you want to save your plant (check all other cruciferous plants close by!), you have little choice. Manual removal is difficult as they hide in lots of folds and wrinkles. And if they are just hosed of, at least some will just crawl up again. Predatory insects can be used, but looking at your photos, I would recommend an insecticide. Ask at your local garden store or similar and always read the label yourself to make sure that it’s suitable for edible plants and to learn about any waiting period that may apply.