Step 1Cut dates in half, remove pits and slice them into thirds. Place them in a small bowl. In a small saucepan, combine baking soda with water and bring to a boil. Pour liquid over dates and allow them to cool.
Step 2Cream butter in bowl of electric mixer on low, 2 to 3 minutes, until softened. Add brown sugar and mix on medium 3 to 4 minutes, until light and fluffy, scraping down sides of bowl as needed.
Step 3Lightly beat eggs, then pour them into mixing bowl, a little at a time, mixing on medium-low until incorporated. Turn mixer to low and add flour, mixing until combined. Stir in date mixture and vanilla. Mixture will be thin.
Step 4Grease 10-inch springform pan with melted butter and set on baking sheet. Pour batter into pan, smoothing evenly. Bake at 350 degrees until spongy, slightly firm to the touch and nicely browned, 30 to 35 minutes. Allow cake to cool, then invert onto a flat surface.
Step 1Melt butter in small saucepan over medium-low heat. Using a small paring knife, split vanilla bean lengthwise and, with back of knife, scrape out pulp and seeds and add to butter along with pod.
Step 2When butter is melted, stir in cream and brown sugar and bring to boil. Reduce heat to low simmer and cook until thickened and a bit sticky, stirring frequently, about 5 minutes. Set aside to cool slightly. Remove vanilla bean pod.
Step 3Spoon sauce over cake, allowing it to run over sides.