Preheat the broiler and put a rack in the middle of the oven. Arrange individual casseroles or a large casserole dish on a baking sheet and set near the stove.
Put the potatoes and the parsnips in a medium pot and cover with water. Bring to a boil, over high heat, then salt the water and cook until the potatoes and parsnips are tender, 15 minutes or so. Drain and return the potatoes and parsnips to the hot pot. Add the horseradish, milk, chives, salt and pepper, to taste, and mash to desired consistency. Stir in 1 cup of the cheese and the egg.
Meanwhile, heat a Dutch oven or large skillet over high heat with extra-virgin olive oil (4 turns of the pan). Add the mushrooms, and the rosemary leaves and cook for 10 minutes. Stir in the carrot and onion and season liberally with salt and pepper, to taste. Cook for 5 minutes more, then stir in the garlic and the kale and season with nutmeg. Cook until the kale wilts, about 2 minutes. Stir in the Worcestershire sauce and the stock and bring to a boil. In a small skillet, over low heat, melt the butter, whisk in the flour and cook for 1 minute, then stir it into the sauce to thicken. Transfer the vegetable mixture to the individual flameproof dishes or a large flameproof casserole. Top with the mashed potatoes, sprinkle with the remaining cheese, and brown under the broiler for 2 to 3 minutes. Remove from the oven and serve.