Preheat the oven to 425°. Heat the goose fat in a large, nonstick skillet over moderate heat until hot but not smoking. Add the mushrooms, season lightly with sea salt, and sauté just until the mushrooms begin to give up their juices, about 5 minutes. Reduce the heat, add the thyme, garlic, half the parsley and half the walnuts. Cook, stirring regularly, for about 1 minute more. Season generously with sea salt and pepper.