DO-AHEAD-TIP: Cook chicken.
Preheat oven to 350 degrees.
Grease a large pan with half the coconut oil and set aside.
Steam broccoli until barely cooked and set aside.
In a sauce pan melt the coconut oil, brown the onions and season with salt and pepper.
Add mushrooms. Sauté until cooked and remove from heat.
Transfer broccoli, mushroom, onions, and shredded chicken into the pan and spread.
In a separate bowl mix broth, coconut milk, eggs, nutmeg with a pinch of salt and pepper and whisk and pour it over the contents of the pan.
Place the pan in the oven and bake for 40 minutes making sure it is done in the middle.
Remove from the oven and let cool for 10 minutes and serve.