Food cravings always puzzle me. Just the other day I had a very very intense craving for nuts. I have not had nuts in about two months. I bought three packets and ate them all. I have always had cravings for different foods.

I used to have fruit cravings, not anymore. Now I only have meat cravings and ice-cream cravings and nut cravings (like the other day). My cravings used to be very intense, they were "overriding" my brain. Now they are much much milder.

I believe Terry Wahls is right about this. She thought people were obese not because they eat too much, but because they don't get enough nutrients. If you lack something in your diet, the brain sends a signal, "get me some nutrients (and a craving is a request for a specific nutrient)" so people start looking for food. And if the food they find is calorie-rich yet nutritionally empty, the vicious cycle perpetuates itself.

I don't have a scientific study to reference but for me, I don't need one.
I think you are right about cravings foods that have a nutrient your body needs. I have had several intense food cravings in my life and I believe for food that contained things my body needed. Most notably I craved beef when I was low iron and salty foods when I was low sodium. Most recently I have had cravings for kale and I believe it is nutrient related. Have also had intense banana cravings related to being dehydrated and another time hungover. I think these were potassium related.
I never have cravings for junkfood either.... which tells me something.
Amazing how well designed we are.

When I started Paleo, I craved Prosciutto ham. I bought a packet (they're so expensive!) and ate it all in a couple of days. I could've easily finished it off in one sitting. I eat sushi/sashimi, so at that time yeah I felt incredibly "primal" but I got a "jolt" of energy I didn't expect to get.

With expectant moms I've heard stories of even eating a little bit of dirt mixed up with water (!!!) and the only conclusion I can get to is yes, there's something that broccoli has that your body needs. The only craving I had when I was expecting once, it was olives. I had to stop working, call someone else to cover for me while I had the cafeteria ladies open a ginormous jar of olives just for me to have a bite! :)

Eat broccoli until the craving stops. My Prosciutto craving lasted for days on end, because I tried NOT to buy it and eat it-I wanted that craving to just go away, but it never did. If it comes back don't be surprised too.