In a mixing bowl, beat the eggs until foamy. Add sugar, salt, baking powder, anisette; beat until smooth. In a small bowl, beat together oil and room temperature butter until well combined. Stir into batter. Gradually add flour, beating only for a short time after flour has been added. Use more or less flour to make soft cookie batter dough. Dough should be soft, but stiff enough to form a smooth shape. Cover; refrigerate dough for several hours. Using a cookie scoop or two tsp., shape the dough into small balls; press bottom of cookies lightly onto lightly greased cookie sheets, while keeping the rounded tops. Bake in a preheated 350 degrees oven for about 15 minutes. The cookies should be crisp but do not brown - they should be very light in color. Using a spatula, transfer cookies to a wire rack to cool. To ice the cookies: In a clean mixing bowl, combine 1 cup confectioners' sugar with 4 tsp. milk and 4 tsp. Karo syrup. Stir until the icing is of a spreadable consistency, adding more milk if required. A few drops of anisette may be added for flavor; a drop or two of food coloring can be stirred in for a pastel-colored icing, if desired. Dip cookie tops into icing, then optionally sprinkle with colored cookie decorations.