In a 2- to 3-quart pan over medium heat, bring dates, granulated sugar, and 3/4 cup water to a boil. Adjust heat to maintain a simmer and stir often until mixture is as thick as jam, 15 to 20 minutes. Stir in sesame seeds. Let cool completely.
In a bowl, with an electric mixer on medium speed, beat butter and brown sugar until smooth; beat in eggs, scraping down sides of bowl as needed. In another bowl, mix flour, baking soda, and salt. Stir or beat into butter mixture until well blended.
Divide dough into four equal portions. Roll one portion at a time between sheets of waxed paper or cooking parchment into a neat 6- by 8-inch rectangle. Pull off top piece of paper and dot dough with a fourth of the date filling, then gently spread to cover dough evenly, leaving a 1/2-inch strip bare along an 8-inch side. From the opposite 8-inch side, roll dough into a cylinder, pulling paper from dough as you roll. Wrap each cylinder airtight in waxed paper. Freeze until firm enough to slice neatly, about 1 1/4 hours.
Unwrap dough. Using a thin, sharp knife, cut cylinders crosswise into 1/8-inch-thick slices (if chilled dough crumbles, let stand a few minutes to soften, then cut). Lay slices 1 inch apart on buttered or cooking parchment-lined 12- by 15-inch baking sheets; if cookies flattened when cut, reshape with your fingers.
Bake cookies in a 350° oven until slightly darker brown, 10 to 12 minutes; if baking more than one pan at a time, switch pan positions halfway through baking. With a wide spatula, transfer cookies to racks to cool completely.