Blend half of the cooked chestnuts with two thirds of the parsley and 2 tablespoons of melted butter in a food processor until well combined. Lay the halibut filets flat on a baking tray, brush the remaining melted butter, season and coat with the chestnut mixture. Bake for 8 minutes; turn off the oven and leave to rest for 4 minutes.
While the halibut cooks, heat a large pan with the groundnut oil and fry the Jerusalem artichokes for 3 minutes. Add the mushrooms and fry for 2 minutes, add the garlic, remaining chestnuts and butter and fry for 2 minutes more.
Transfer to a hot tray and add the cubes of butter to the pan, heat until the butter turns nutty brown then add the chicken stock and remaining chopped parsley.
Serve the halibut surrounded with the mushroom mixture and spoon the sauce over the top.