I know vegetables need to be checked carefully for bugs. What about frozen cauliflower or broccoli? How does one check them?

ב"ה Shalom Cauliflower and broccoli must be carefully checked for bugs as you mentioned even when fresh. I suggest looking at the books of Rav Moshe Vaya on how to examine them or some other equivalent book or website. Checking the vegetables after defrosting makes checking even more difficult because the vegetables become soft. Therefore, my strong suggestion would be to buy cauliflower or broccoli from companies with good kosher authorization in which the cauliflower or broccoli are properly cleaned and examined before freezing and are bug free. All the best