In a large bowl, combine the ground beef, coconut aminos, ½ teaspoon salt, and ½ teaspoon pepper. Divide the meat mixture into 4 portions, shaping each into a patty.
In a large skillet over medium-high heat, melt 1 ½ teaspoons ghee. Add the beef patties and cook for 3 minutes per side. Remove from the skillet and set aside.
Melt the remaining 1 ½ teaspoons ghee in the skillet. Stir in the mushrooms and onions. Cook for 5 minutes, stirring frequently.
Mix together the beef broth, wine, and arrowroot powder. Stir into the mushroom mixture and cook until the broth has begun to thicken.
Move the onion mushroom mixture to the side and return the beef patties to the skillet. Cover, reduce heat, and cook for 5 minutes, or until beef is cooked through.
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Notes
For those who are not paleo and would still like to try this recipe the following substitutions can be made: