Cream the butter and sugar using an electric mixer. Add the egg and vanilla and mix well.Whisk in flour, baking soda, and salt. Stir with a mixer until combined. Incorporate with your hands to finish.
Divide the dough in half, wrap each portion tightly in plastic wrap, and chill in the fridge for 30 minutes.
Meanwhile, prepare the date filling. Mix pitted dates with water and sugar in a small saucepan. Place it over medium-low heat until the dates have softened, the sugar has dissolved, and the mixture has thickened. Stir continuously. Once you achieve a thick jam consistency, incorporate chopped walnuts and remove them from the heat. Set it aside to cool down.
Roll each half of the dough on parchment paper with a floured rolling pin into an 11×7" rectangle.Divide the cooled date and nut filling between the two rectangles and spread evenly over the dough. Beginning at the wide end, use parchment paper to help roll the dough up tightly. See pictures in the post for reference. Pinch the edge to seal. Wrap the logs in the parchment paper and refrigerate for several hours.
When ready to bake, preheat the oven to 400F and slice the logs into 1/4" slices. Place on a lightly greased baking sheet and bake for 8-10 minutes, or until lightly browned.