Preheat oven to 350 degrees. Butter ten 4-ounce ramekins; set aside. In a medium bowl, whisk together flour, baking powder, and baking soda; set aside.
In a small saucepan, combine dates, and 1 cup warm water. Simmer until most of the water is evaporated, about 5 minutes. Transfer to a small food processor, and process until smooth; keep warm.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and sugar on medium speed until light and fluffy, about 2 minutes. Slowly add the eggs, and beat to combine. Scrape down sides of bowl. Add the flour mixture, and beat until fully combined.
With machine running, add date purée, a little at a time, beating to combine after each addition. Divide evenly between prepared ramekins, filling each about three-quarters full. Bake until a cake tester inserted into the center comes out clean, 20 to 30 minutes.
Cool to room temperature, slice off top, and discard. Cut in half horizontally, and layer with sauce. Serve immediately with ice cream, if desired.