For the icing, chop raisins and figs, place in a small bowl. Stir in brandy; let stand 1 hour. Combine fruits, soaking liquid, pecans, and candied cherries. Stir in creamy white frosting; set aside.
Beat butter and shortening in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add half of the flour. Beat in sugar, milk, lemon peel, and almond extract. Beat in remaining flour until combined.
Drop by rounded teaspoons 2 inches apart on an ungreased cookie sheet. Bake in a 375 degree F oven for 10 minutes or until very lightly brown around edges. Transfer cookies to wire racks to cool. Frost each cookie with about 1 tablespoon of the icing. Makes about 36 cookies.