Peel the Jerusalem artichokes, potato, and apple and cut into rough 2-inch pieces. As you are prepping, drop them in lightly salted water so they don’t discolor. Drain the vegetables and place in a pot with 1/2 cup of the cream and just enough water to cover the vegetables. Boil until tender.
Drain purée using a food mill or potato ricer. Do not put in a food processor or blender, as it will come out gummy. Meanwhile, heat the remaining cream with the butter. When melted, stir into the purée lightly (you don’t want to overwork it).
If you want to make it ahead, you can cool the mixture down and then reheat in a hot 375° F oven. Place the potatoes in a Dutch oven or roasting pan, drizzle a couple tablespoons of water around the edges and a pinch of salt, and heat up for about 15 minutes, until the purée is hot throughout, and personally, I like to let it get a bit golden on the top.