In a large skillet over medium heat, heat coconut oil. To the skillet, add the chicken and brown for 5 minutes. To the chicken, add the next 3 ingredients (leek through cauliflower) and cook for 5 minutes, until chicken is cooked through and vegetables are starting to get tender. In a large baking dish, pour the chicken mixture.
In a large bowl, whisk the remaining ingredients and pour over the chicken mixture. Place baking dish in the oven and bake for 20 minutes, until eggs have set.