I occasionally feed broccoli to my tortoises. Some will eat it some won't. It is a cruciferous vegetable, which means it contains goitrogens. So fed to extreme it might cause your tortoise to have goiter.
I keep leopards, Manouria, desert, redfooted, yellowfooted, Aldabran, Texas and sulcata. Of those, the YF and RF will not eat broccoli. The ones who will eat it only get it about once a month.
expert said broccoli is not so good. i've fed my star baby broccoli and on a second try she didn't put any interest on it. just leave the doubtful one.