Make the dough: Whisk the flour, granulated sugar and salt in a medium bowl. Beat the cream cheese and butter in a large bowl with a mixer on medium-high speed until fluffy, about 3 minutes. Reduce the mixer speed to low and beat in the flour mixture until the dough just comes together. Increase the speed to medium high and beat until combined, 30 seconds to 1 minute. Transfer the dough to a sheet of plastic wrap; shape into a disk. Wrap and refrigerate until firm, at least 1 hour or overnight.
Meanwhile, make the filling: Combine the prunes and brandy in a small microwave-safe bowl. Microwave until the prunes soften, about 1 minute; let cool slightly. Transfer the mixture to a food processor and add the apricot preserves, cinnamon and pepper; puree. Scrape into a
small bowl and refrigerate until firm, at least 30 minutes or overnight.
Line a baking sheet with parchment paper. Cut the dough in half; roll out each half into a 6-by-12-inch rectangle on a floured surface. Transfer the rectangles to the prepared pan; refrigerate until slightly firm, at least 20 minutes.
Preheat the oven to 350 degrees F. Spread the prune mixture over the dough, leaving a 1-inch border on one long side of each rectangle. Starting with the opposite long side, gently roll each rectangle into a tight log and position seam-side down. (If the dough becomes too soft to work with, refrigerate briefly.) Brush the logs with the beaten egg and sprinkle with the coarse sugar. Refrigerate until firm, about 30 minutes.
Trim the ends of each log, then slice each into twelve 1-inch-thick rounds. Arrange 1 inch apart on the prepared pan, seam-side down. Bake, rotating the pan halfway through, until the cookies are golden, 30 to 35 minutes. Transfer to a rack and let cool on the pan.