Inspect the undersides of broccoli, cabbage and kale leaves, squishing any tiny, yellow, almond-shaped eggs that appear by themselves. But leave the ones that appear in clusters, which likely belong to ladybugs.
Smudge out the tiny white rows of eggs with your fingers every few days in summer, or just harvest the young leaves for tender braised greens to stay ahead of the leaf miners.
You can also apply Bacillus thuringiensis (B.t), a commercially available bacterium, to plants when caterpillars are feeding. Be careful, B.t. is toxic to many different types of caterpillars.