For date filling: In small saucepan combine dates, nuts, water, the sugar, and lemon juice; bring to a boil over medium heat, stirring occasionally. Reduce heat; simmer until the liquid is absorbed and dates and nuts are spreadable. Transfer to a bowl; let cool to room temperature.
For dough: In a bowl combine the flour, baking powder, and baking soda. In a large mixing bowl beat butter, brown sugar, and salt with an electric mixer on medium speed about 3 minutes or until the mixture is smooth and creamy, scraping bowl as needed. Add the egg and beat for another minute or until combined. Add dry ingredients all at once, beating on low speed until combined. (You'll have a soft dough that cleans the sides of the bowl.)
Turn dough out onto a piece of parchment paper, and shape it into a rectangle. Cover with another piece of parchment and roll the dough into a 1210-inch rectangle. (While rolling, peel paper away from the dough often so it doesn't leave creases.) Slide dough, still between paper, onto a baking sheet and refrigerate at least 2 hours or freeze at least 1 hour.
To fill and roll: Leave cold dough on the counter about 10 minutes or until it's supple enough to bend without cracking. Peel off the top sheet of parchment from the dough. Flip onto a clean sheet of parchment paper. Peel off remaining sheet of parchment. Position dough so a long side is parallel to you. Spread filling to within 1 inch of top and 1/2 inch of short sides. Starting with long edge closest to you, use the paper to lift and roll the dough into a log, keeping it compact. (The ends will be ragged.) Wrap the log in plastic wrap or waxed paper and refrigerate at least 1 hour.
To bake: Position the racks to divide oven in thirds; preheat to 350 degrees F. Line two baking sheets with parchment paper. Unwrap and place log of cookie dough on a cutting board, and trim ends until you can see spirals of filling. Using a thin sharp knife, cut the log into 1/2-inch slices. (Don't worry if there are gaps between the filling and the dough; they'll fill in as they bake.) Place about 11/2 inches apart on baking sheets. Chill the remaining log.
Bake for 15 to 17 minutes (rotate baking sheets top to bottom and front to back after 8 minutes) or until cookies spread, puff, and brown lightly (they should still be soft if gently poked). Cool on baking sheets 2 minutes; carefully transfer to wire rack to cool. Serve cookies warm or at room temperature. Bake the remaining cookie slices on a cool baking sheet.