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Toss the anise seeds into a dry pan over low heat and toast until fragrant, stirring frequently (do not burn!) Crush slightly with the back of a spoon.
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Combine the masarepa, warm water, salt, toasted anise seeds and sugar, mixing thoroughly. Let mixture stand, covered, for five minutes to allow the cornmeal to fully hydrate.
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Form 8 small balls with the dough. Place each ball between 2 sheets of wax paper and with a dinner plate, cutting board, frying pan, or any other flat-bottomed object, and flatten to ¼ inch.
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Heat the vegetable oil in a large heavy pot to 350 F. Add the arepas in the heated oil one by one, fry for 3 minutes or until golden brown on both side, turning over once about half way through. You'll know it's time to turn it when the edges get golden, just like a pancake.
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Using a slotted spoon, carefully remove the arepas from the oil and drain on paper towels.
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Proceed to stuff your face, and prepare for a nap.