In a large bowl, mix the first 4 ingredients (turkey through oregano). Form turkey mixture into patties. Place burgers on the grill pan and cook for 5 minutes on each side, until burgers are cooked through.
In a large skillet over medium heat, heat coconut oil. To the oil, add the coconut aminos and the mushrooms. Cook for 5 minutes on each side, until tender.
In a medium bowl, mix the next 4 ingredients (avocado through lime juice) with sea salt and freshly ground black pepper to taste.