Preheat oven to 350 degrees. Butter and flour a 6 cup Bundt pan, or 6 one cup Bundt pan molds.
Bring dates and 1 1/4 cups water to boil in a medium heavy saucepan with tall sides. Remove from heat; stir in baking soda (mixture will become foamy). Set aside to cool.
Whisk 1 1/2 cups flour, baking powder, and salt in a small bowl. Using an electric mixer, beat 1/4 cup butter, sugar, and vanilla in a large bowl to blend (mixture will be grainy). Add 1 egg; beat to blend. Add half of flour mixture and half of date mixture; beat to blend. Repeat with remaining 1 egg, flour mixture, and date mixture. Pour batter into pan (molds).
Bake until a tester inserted into center of cake comes out clean, 40-45 minutes. Let cool in pan on a wire rack for 30 minutes. Invert pudding onto rack. Can be made one day ahead. Cover and let stand at room temperature.
Sauce: Bring sugar, cream, and butter to a boil in a small heavy saucepan over medium heat, stirring constantly. Continue to boil, stirring constantly, for 3 minutes. Remove from heat; stir in brandy and vanilla. Can be made 4 hours ahead. Let stand at room temperature. Rewarm gently before using.
Cut cake into wedges. Serve warm with sauce and whipped (or ice) cream.