Bring a large pot of lightly salted water to a boil. Add cabbage and briefly blanch, about 3 minutes. Drain and rinse under cold water to stop the cooking process. Shred leaves finely.
Melt butter in a pot over medium-low heat and cook shallots until soft and translucent, about 5 minutes. Dust with confectioners sugar. Add blanched cabbage and cook, stirring occasionally, over medium heat, for about 3 minutes. Stir in horseradish and cream and bring to a simmer. Season with salt, pepper, cayenne, and nutmeg. Add pears and cook until heated through, about 3 minutes. Serve immediately.
