PREHEAT the oven to 400°F.
BRING a large pot of salted water to a boil. Add the potatoes and cook until fork-tender, about 20 minutes. Drain well and return to the pot.
ADD the melted ghee and coconut milk. Mash until the consistency is light and fluffy. Season with salt and pepper to taste. Set aside.
IN a large oven-safe skillet (see Note) over medium heat, cook the bison, breaking it up with a wooden spoon, until browned, 7 to 10 minutes. Drain any excess fat. Add the onion, carrots, celery, green beans, and a pinch of salt and pepper and cook, stirring, until fragrant and softened, 3 to 5 minutes. Stir in the garlic, thyme, and parsley.
IN a separate bowl, mix the arrowroot starch with 1 cup of the beef broth until it is fully dissolved and there are no lumps. Add to the bison along with the remaining 1 cup broth, the coconut aminos, and tomato paste; mix well. Bring to a simmer and allow the sauce to thicken for about 10 to 15 minutes. Season with more salt and pepper if necessary.
SPREAD the mashed sweet potatoes evenly over the bison mixture. Bake for 20 to 25 minutes, until the potatoes are golden and the edges are bubbling. For even browning on the top, broil on high for 3 to 5 minutes. Sprinkle with fresh parsley and serve.
NOTE: If your skillet is not oven-safe: In the last step, transfer the bison mixture to a baking dish before topping with the mashed potatoes.