Peel, wash and slice the carrots. Wash the meat, dab dry and cut each fillet in half crosswise. Heat the oil in a large pan. Brown the meat well in it. Fry over medium heat for about 4 minutes, turning.
Mix 1 tablespoon cream cheese and crème fraîche, season to taste with salt and pepper. Mix the rest of the cream cheese and milk, season with salt, pepper and nutmeg. Season meat with salt and pepper, remove from the pan. Fry the carrots in hot frying fat while turning, season with salt and pepper. Mix in gnocchi. Pour cream cheese milk over the gnocchi. Add meat again and simmer covered for about 8 minutes.
Wash parsley, shake dry and chop. Sprinkle on the chicken pan and serve with a crème fraîche dip.