Combine flour and baking powder in a large mixing bowl; stir well. Cut in shortening with a pastry blender until mixture resembles coarse meal. Make a well in center of mixture, and set aside.
Combine sugar, milk, and vanilla in a small saucepan. Cook over medium heat, stirring constantly, until sugar dissolves. Remove from heat, and gradually stir in eggs. Pour into reserved flour mixture, stirring just until dry ingredients are moistened.
Knead 3 to 4 times on a lightly floured surface. Roll to 1/4-inch thickness; cut into 1 1/2-inch squares. Place a fig in the center of each square; press dough around fig.
Place cookies, seam side down, on greased cookie sheets. Bake at 350° for 12 to 15 minutes. Remove from cookie sheets, and cool completely on wire racks. Spread frosting over tops of cookies.