2. In a small bowl, combine the dates, walnuts, apricot preserves, and cinnamon. Divide the mixture equally into 40 balls. With your hands, roll each ball into a log about 2 inches long. Set the logs aside.
3. Unfold the phyllo pastry on a large work surface and cover it with a barely damp kitchen towel.
4. Keeping the unused pastry covered with the towel while you work, carefully remove the top pastry sheet and brush it generously on one side with some of the butter. Set a second pastry sheet on top of the first sheet, brushing again with some of the butter. Repeat with a third sheet and more butter. Using a sharp knife, cut the stacked and buttered sheets into 8 rectangles about 7 x 4 1/2 inches each.
5. To form "cigars," place a date log parallel to a long side of each phyllo rectangle, setting it about 1 inch from edge and folding that edge over the log. Fold both of the short sides in over the ends of the log, then roll the log up. As you work, place the rolled pastries on a baking sheet and brush with more of the melted butter. Bake the pastries for about 30 minutes, or until golden. Remove the pastries from the oven and cool for 1 minute on baking sheets. Transfer the pastries to a wire rack and brush or drizzle them lightly with the hot syrup and sprinkle with some of the sesame seeds. Cool.
6. Repeat the process with the remaining phyllo sheets, date logs, syrup and sesame seeds.