To make the filling, in a food processor, combine the figs, dates and raisins and process to finely chop. Place the mixture in a medium bowl, add remaining filling ingredients and stir to combine. Cover 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 45 minutes.
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 12-inch square. Cut the dough into 4 by 3-inch rectangles. Spoon 2 tablespoons of filling 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. With a floured knife, cut the logs crosswise into 1 1/2-inch-wide slices and arrange 1/2-inch apart on the prepared baking sheets. Brush with egg wash and decorate with colored sprinkles. Bake until golden brown, about 20 minutes.
Transfer to wire racks to cool. Serve warm or at room temperature.