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 tbs milk and 4 tbs 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.