Add inch of water to the bottom of a steamer pot, then add the steamer basket and lid on top, and boil the water over high heat.
Once the water is boiling, add 4 cups of chopped broccoli to the steamer basket, place the lid on top, steam for 4-5 minutes, then remove the steamer pot from the heat.
Crack 6 eggs in a mixing bowl, then whisk together.
Add 1/4 tsp of black pepper, 1/4 tsp of sea salt, 1/4 tsp of nutmeg, and 1 1/2 cups of canned coconut milk to the mixing bowl, then whisk it all togther.
Over medium heat, melt 1 tbsp of coconut oil in an oven-safe pan, ensuring the coconut oil covers the entire surface of the pan.
Add the egg mixture to the pan, turn off the heat, then top with the steamed broccoli.
Add the oven-safe pan to the pre-heated oven and bake for 20-25 minutes, or until the mixture sets in the middle.
Remove the pan from the oven, slide the broccoli quiche onto a cutting board, then cut into 4 pieces, and add it to a plate.