Beat eggs until light and frothy in a large mixing bowl. Add persimmon and sugar, beating well. Combine flour, cinnamon, nutmeg, and salt; stir well. Add to egg mixture, beating well. Dissolve soda in buttermilk; add to pudding mixture. Stir in vanilla and pecans.
Pour batter into a wellgreased 1 1/2-quart pudding mold, and cover tightly with lid. Place mold on rack in a large kettle; add boiling water, filling kettle half full. Bring to a boil. Reduce heat; cover and simmer 2 hours.
Remove mold from kettle; remove lid from mold to allow steam to escape. Cool 10 minutes. Loosen pudding from sides of mold, and invert onto a serving dish. Serve warm with hard sauce.