In a mortar and pestle or a spice grinder, grind the anise seeds until relatively fine. Whisk together the flour, cornmeal, baking powder, salt, and anise seeds. Set aside. Beat the butter and sugar until light and fluffy. Add the eggs one at a time until they are incorporated. Mix together the milk and absinthe with a small handful of orange zest (Use more if you want the orange flavor to shine more. I used about 1/2 t.) Stir half the dry ingredients into the beaten butter. Then add the milk and absinthe mixture. Stir in the remaining dry mixture, being careful not to over mix. They hardly rise at all so you can fill your liners almost all the way to the top. Bake for 30 min at 350 degrees.
Absinthe Glaze Instructions
Stir the sugar and the absinthe. You do NOT want the sugar to dissolve in the absinthe. As you can see in the picture, the glaze had big sugary clumps. Poke holes in the cupcakes and drizzle the glaze into the holes and all over the tops of the cupcakes. All of the glaze should be used when you are done.