The jury is still out on thyocyanates (goitrogens just refers to any compound that can damage the thyroid, lets be more specific) and thyroid function.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4135245/

The cited article here is a review, in which they discuss the findings of a variety of articles. Some of the articles published on the subject found a positive correlation between thyroid cancer and consumption of cruciferious vegetables (like broccoli), others saw no correlation, some saw a correlation, but only if the person had an iodine deficiency in their diet. At this point I don't think there is a very clear link between broccoli consumption and thyroid troubles.

you should be aware of how long you cook your broccoli

well if you want to break down the thyocyanates then yes longer cook times will degrade the compounds, however these very same compounds are the ones discussed in this article with arthritic protective activities (Solforaphane is one of these compounds, and is the subject of this entire post!)

Also, why would you put cheese on broccoli? You're ruining it! ;-)

I like to do lots of things with it. Sometimes I like to add cheese with broccoli, its tasty. Roasting broccoli with some fresh garlic is also tasty. I mean there are a lot of things you can do with it other than just plain old steamed (which is also fine). I it raw too. :)