In a medium saucepan combine the water, butter, brown sugar, and salt. Bring to boiling over medium heat. Add flour and anise seed all at once, stirring vigorously with a wooden spoon. Cook and stir until mixture forms a ball and pulls away from the sides of the pan. Remove from heat. Cool for 10 minutes. Add egg, almond extract, and anise extract, beating well with a wooden spoon.
Preheat oven to 300 degrees F. Transfer mixture to a decorating bag fitted with a large open star tip. Line a large baking sheet with waxed paper. Pipe 4x1-inch logs onto prepared baking sheet.
In a deep saucepan heat 3 inches of oil to 375 degrees F. Fry logs, a few at a time, in hot oil about 2 minutes or until golden brown on both sides, turning once. Drain on paper towels. Keep warm in oven while cooking remaining churros.
In a shallow dish place granulated sugar. Roll warm churros in sugar to coat.
For the chocolate sauce, in a small microwave-safe bowl combine the chocolate pieces and whipping cream. Cook on 100% (high) power for 1 minute. Whisk mixture until all the chocolate is melted and mixture is smooth. Stir in the coffee liqueur. Serve churros with chocolate sauce.