Preheat the oven to 220°C (approximately 425°F). Cut the chestnuts crosswise and roast until the shell opens. Toast until golden brown, about 30 minutes. Peel the chestnuts. Set 8 aside and keep warm. Coarsely chop the rest.
Peel the potatoes, rinse and cut into large pieces. Cook in salted water and drain.
Sweat the shallots in hot butter until translucent. Add the potatoes and chopped chestnuts. Stir in cream and 100 gram (approximately 7 tablespoons) of butter and bring to a boil. Season with lemon juice, salt, pepper, and nutmeg. Puree or mash and keep covered and warm.
Clean the cabbage and cut into quarters. Remove the stem and cut into fine strips. Saute in the remaining butter. Add 1/2 cup of water, salt, and pepper. Cover and bring to a simmer. Let cook for 15 minutes. Stir in the creme fraiche and parsley. Season with nutmeg.
Arrange the cabbage with the chestnut-potato puree and serve with the roasted chestnuts.