In a large bowl, cream butter and sugar until light and fluffy. Beat in eggs and vanilla. Combine the dry ingredients; gradually add to creamed mixture. Stir in the carrots, potatoes, raisins, dates and nuts.
Pour into a well-greased 6-cup pudding mold or metal gelatin mold. Cover with foil. Place on a rack in a deep kettle. Add 1 in. of boiling water to kettle; cover and boil gently for 1-1/4 to 1-1/2 hours or until a toothpick inserted near the center comes out clean, replacing water as needed. Let stand for 5 minutes before unmolding.
Meanwhile, in a small saucepan, combine the sugar, cornstarch and salt. Stir in water until smooth. Bring to a boil over medium heat; cook and stir for 1-2 minutes or until thickened. Remove from the heat. Stir in the butter, vanilla and nutmeg. Serve with warm pudding. Yield: 6-8 servings.