Here's a quick and easy way of getting your iodine, unsupplemented ...
Dried sea vegetables, procured from the supermarket Japanese section, steeped in bouillon (or bone broth if you have some) and spiced up with ginger and chilli. Make more interesting with some mushrooms - enoki variety in my case.
Mushrooms are packed with yet more antioxidants, making is one seriously heart-healthy starter.
Sea vegetables are not only a fantastic source of iodine, but possibly a unique source of vanadium. Reading up, vanadium appears to play a multi-faceted role in regulation of carbohydrate metabolism and blood sugar.
If somebody with a better grasp of biochemistry than me (that's everyone, then) can offer further insight, I'd be very grateful. Let's hear from you in the comments.