Make the Filling: In a bowl, combine the figs with 4 tablespoons of brandy and let soak overnight or up to 4 weeks.
In a food processor, combine the soaked figs, the remaining 2 tablespoons brandy, and all the remaining filling ingredients. Process until chopped and well combined. (Alternatively, run all the ingredients through a meat grinder. Some Italian women bring their filling ingredients to the butcher and have him grind it for them.) Keep chilled until ready to use.
Make the Pastry: In a food processor, combine the flour, sugar, baking powder, and salt and pulse to mix. Add the butter and pulse until it looks like fine crumbs. In a small bowl, whisk together the 2 eggs and milk. While the motor in running, pour the liquid through the feed tube until just combined and a dough is formed. Form the dough into a disk and chill 30 minutes.
On a floured work surface, roll out the dough 1/8-inch thick. With a sharp knife or pizza cutter, cut out large (3-inch long) almond shaped pieces from the dough. Transfer the pieces to a sheet pan; then chill.
To form the cookies, have ready the filling, the chilled dough pieces, the egg wash with a pastry brush, and a sharp knife. Paint the edges of the dough pieces with egg wash and place 1 teaspoon of filling shaped into an oval in the center of half the pieces. Top each with a second piece of dough and carefully pinch the edges together to seal. Trim the excess dough from around the edges.
Make each dough package look like a bird or fish, by shaping and cutting decorative lines. You can split 1 end to look like a tail, carve rows of lines to look like feathers or fins, cut a curved line for the gills or beak opening, and a hole for the eye. (There are many different shapes they're made into, such as wreaths, slippers, and crescents.) Re-chill the cookies
Preheat the oven to 350 degrees F.
Brush the cookies with the egg wash. Bake the cookies until lightly golden brown, about 20 minutes.
Meanwhile make the Icing: In a bowl, whisk together all the ingredients.
Toss the cookies with the icing while they're still hot and sprinkle with the colored sprinkles, or leave them plain. The icing makes the cookies look like porcelain when they're done.