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Combine the flour, sugar and heaping tablespoon of baking powder.
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In another bowl whisk together the eggs, vegetable oil and anise extract.
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Combine wet and dry ingredients. Dough will be sticky, add up to an extra 1/4 cup of flour if needed.
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Shape cookies as desired (lightly oiled hands will help). One way to do it: roll about 2 tablespoons of dough between hands until you have a rope, fold rope in half and twist. You can also just make little dough patties.
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Place on ungreased cookie sheets. Bake at 350 degrees for 10 minutes (this is good for dark nonstick sheets, you might need to bake a little longer if using airbake sheets).
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Remove from cookie sheets and let cool completely.
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To make icing, melt butter then add milk. Gradually mix in powdered sugar. Add more sugar or milk until at desired spreading consistency.
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Frost cookies. Icing will harden quickly so add non-pareils or other sprinkles immediately after frosting each cookie.