Preheat oven to 350 degrees. Line a 13 by 9-inch baking pan with parchment or waxed paper.
Combine the dates and water in a high sided saucepan and bring to a boil. Turn off the heat and gradually stir in the baking soda (it will foam up quite a bit), and set aside.
In a bowl, combine the flour and baking powder. In the bowl of a mixer, cream the butter until fluffy. Add the sugar to the butter, and cream until fluffy. Without stopping the mixer, add 2 of the eggs and mix until combined. Add the remaining 2 eggs and vanilla and mix until combined. Add about 1/3 of the flour mixture and 1/3 of the dates and mix until combined. Repeat until all the flour mixture and the dates are incorporated into the batter. Pour into the baking pan and bake about 40 minutes, until firm and set in the center. Let cool in the pan. When cool, turn out of the pan onto a baking sheet and peel off the parchment paper. The recipe can be made through this step up to 2 days in advance.
Butterscotch Sauce: Combine the brown sugar, butter, half-and-half, and brandy in a saucepan and bring to a boil. Boil 3 minutes, until combined. Remove from the heat and stir in the vanilla.
When ready to serve pudding, preheat the oven to 400 degrees. Pour the sauce evenly over the top of the cake. Bake until the sauce is bubbly and cake is heated through, about 5 minutes. Meanwhile, whip the heavy cream into soft peaks with the mixer. Cut the cake into squares and serve with whipped cream.