Gather the ingredients.

To make the filling: Working in two batches with 1/2 of the figs and 1/2 of the dates at a time, pulse dried fruit in a food processor until finely chopped; transfer to a bowl.

Use a vegetable peeler to peel orange zest into the empty food processor. Juice the orange until you have 3 tablespoons juice; add it to the food processor. Add raisins, pecans, honey, brandy, cinnamon, cloves, allspice, and nutmeg and process until finely mixed.

Add fig mixture and process until well combined, adding water 1 tablespoon at a time as needed to reach a thick consistency. Refrigerate filling for 8 hours to overnight.

To make the dough: Combine flour, sugar, baking powder, and salt in a food processor and process for 5 seconds to combine. Add butter and shortening and pulse until crumbly. Add milk, egg, vanilla, and almond extract and process until a dough forms.

Turn dough onto a well-floured surface and knead until smooth. Wrap in plastic wrap and refrigerate for 1 to 2 hours.

When ready to bake, preheat the oven to 375 degrees F (190 degrees C). Line baking sheets with parchment paper. Turn dough onto a floured surface and cut into 4 pieces. Roll one piece into a 4x12-inch rectangle, about 1/8-inch thick. Trim off any excess to form straight edges and save to make more cookies.

Place about 1/4 of the filling in a 1-inch-wide log down the length of the rectangle, just to the right of the center line. Dampen the edges of the dough with water and fold the right edge over the filling. Continue rolling the dough toward the left edge, then rock back and forth gently to seal the seam and lengthen the log slightly. Cut the log into 2- to 2 1/2- inch pieces. Make 2 or 3 slits in the top of each cookie to allow steam to escape. Transfer to prepared baking sheet; repeat with remaining dough and filling.

Bake in batches in the preheated oven until golden on the bottom and cooked through, 12 to 14 minutes. Remove from the oven and let cool completely.

Meanwhile, prepare the icing: Whisk powdered sugar and milk together in a bowl until smooth. Divide icing into thirds in 3 small bowls. Color one bowl with red food coloring to make pink icing, color another bowl with green food coloring to make green icing, and leave the remaining icing white.

Dip each cooled cookie into a different color icing and allow excess to drip off. Place iced cookies on parchment paper and decorate lightly with sprinkles. Allow to dry for at least 20 minutes before serving.