Broccoli and other vegetables that are members of the brassica family such as cabbage, bok choy and brussel sprouts should always be avoided and never fed to your turtle as they are problematic when given to turtles, especially when given in excessive amounts.
When fed excessive amounts of things such as broccoli, turtles usually get kidney disease and goiter. Things such as turnips, soybeans, radishes, and rapeseed also contain goitrogens that can lead to disease so they are better off avoided altogether or fed very sparingly. However one thing to note is that it has been suggested that the addition to kelp in a turtle’s diet has been known to possibly reverse the goitrogenic effect that the brassicas have on the turtle’s body.
Both aquatic and terrestrial turtles have similar feeding habits although aquatic turtles prefer to eat meat when they mature. Older turtles eat less meat because they require less protein. Variety is the main key to your turtle’s diet. Calcium is another important key.
If your turtle is hungry and the only thing you have in the house is broccoli, it will not necessarily harm your turtle to eat it just this once or on rare occasion, but it is best to not let it become a habit as it is bad for your turtle’s overall health in the long run.