Make pudding: Preheat oven to 400°F. Grease 6 6-oz. ramekins or custard cups with butter or cooking spray. In a small bowl, combine flour, baking soda and salt; mix well.
With an electric mixer, cream together butter and brown sugar until fluffy, scraping down sides of bowl as necessary. Add eggs one at time, beating well after each, then add vanilla and beat until smooth. Stir in flour mixture. Fold in dates.
Divide batter among ramekins. Place ramekins on a baking sheet and bake until cakes are no longer gooey but moist crumbs cling to a toothpick inserted into center of a cake, 20 to 25 minutes. Transfer to a wire rack and let cool 5 minutes, then turn cakes out onto wire rack and let cool slightly.
Make sauce: In a small pan over medium heat, melt butter. Add brown sugar and vanilla and cook 5 minutes, stirring, until bubbling and deep brown in color. Gradually add cream to sugar mixture, stirring, and cook 2 minutes longer. Remove from heat. (Sauce will thicken as it cools; re-warm over low heat.)
Serve cakes warm, with a generous amount of sauce poured over top. Serve any extra sauce on the side.