Place dates and water in a small saucepan. Stir. Bring to a boil over high heat.
Remove from heat and stir in the baking soda and butter. The baking soda will get a tiny bit foamy and the butter will begin to melt. Set aside for about 25 minutes to cool.
While the date mixture is cooling, prepare the baking pan. (The original recipe called for an 8-inch springform pan, but I only had a 9-inch springform pan. It worked fine - the cake was not quite as tall as it would have been in an 8-inch pan and also the cooking time was somewhat decreased.) Grease the pan well (I used shortening). Line the pan with parchment paper. To do this, I traced the bottom of the pan onto the parchment paper, then cut out the circle and placed it in the bottom of the pan. For the sides, I cut a strip of parchment paper an inch or two taller than the pan height of the pan edge, then pressed the parchment around the inside perimeter of the pan. See the pictures in the blog post for a tutorial. Set prepared pan aside.
Preheat oven to 350-degrees F. Adjust the oven racks to the lower third of the oven so that the top of the pudding will be in about the center of the oven.
In a medium bowl, mix together the flour and brown sugar. Break up any clumps of brown sugar which may form. Set bowl aside.
Put the cooled date mixture in a food processor or blender. Pulse a few times to break down the dates. This will form a thick, somewhat chunky date paste.
Add the eggs and the vanilla to the date mixture. Process until smooth.
Add the date mixture to the flour/brown sugar mixture. Fold together gently just until combined.
Pour into prepared springform pan. Bake for about 50 minutes or until the pudding springs back when lightly pressed in the center. Remove pudding from oven and place on a cooling rack for 10 minutes.