Preheat the oven to 375 degrees F. Lightly grease 2 large baking sheets. On a lightly floured surface, one at a time, roll out each piece of dough into a thin 12-inch square. Cut the dough into 4 by 3-inch rectangles.
To make the filling, combine the figs, dates and raisins in a food processor, and pulse to finely chop into a very thick paste. Place the mixture in a medium bowl, chop the nuts to small pieces and add them plus the remaining filling ingredients to the paste. Use your hands to combine into a VERY thick paste. Ziploc bag and refrigerate for at least 8 hours.
To make the dough, in a large bowl combine the flour, sugar, baking powder, and salt and whisk to combine. Add the butter and blend with your fingertips until most of mixture resembles coarse meal. In a medium bowl, beat the egg, milk and vanilla together. Add to the dry mixture and stir to make a rough dough. Turn the dough out onto a lightly floured surface and knead until smooth, about 5 minutes. Cut the dough into 4 pieces, cover, and refrigerate for at least 45 minutes.
Now prepare to get gooey: use your hands to grab off 2 tablespoons of filling and roll it into a long rod shape. Place the rods down the center of each rectangle. Fold the long sides of each rectangle inward to the center to enclose the filling; pinch the edges to seal. Turn the cookies seam-sides down and press gently to flatten the seams.
Arrange the logs 1/2-inch apart on the prepared baking sheets. Brush with egg wash or brush tops with Jalob syrup. Bake until golden brown, about 20 minutes. Transfer to a wire rack to cool, sprinkle with powdered sugar and cinnamon.
Serve logs cut in halves, or as one-inch long pieces. Keeps well when frozen.