Season the ground beef with salt and pepper and form into 4-5 burgers.
Heat the avocado oil over medium heat in a large pan and add the burgers. Cook for 4-5 minutes on each side or until the internal temperature reaches 160-165 F. Set aside, leaving at least 2 tbsp of fat in the pan (adding more if needed).
Reduce to heat to medium-low. Add the mushrooms and cook in a single layer, undistured for 3-4 minutes or until lightly tender. Add the onion and toss to saute for 5-6 minutes, or until the onion is slighly caramelized.
Combine the broth, coconut aminos, mustard, apple cider vinegar, arrowroot starch and seasonings in a bowl and stir to combine. Pour the mixture into the pan and reduce the heat, allowing to thicken for 3-4 minutes.
Once the gravy is thick, add the burgers back to the pan and spoon the gravy over the burgers. Serve topped with chopped parsley!