Combine the flour, 1/2 cup cocoa powder, 1/3 cup confectioners¿ sugar, the baking powder and salt in a food processor and pulse to combine. With the machine running, add the egg, Sambuca, melted butter and anise extract. Add the milk, 1 tablespoon at a time, pulsing until clumps of dough begin to form. Turn the dough out onto a floured surface and knead until it just comes together. Transfer to a sheet of plastic wrap and shape into a disk. Wrap and refrigerate until firm, about 30 minutes.
Fill a medium Dutch oven or heavy-bottomed pot with 2 to 3 inches of vegetable oil. Heat over medium heat until a deep-fry thermometer registers 350 degrees F. Meanwhile, divide the dough in half. Working with 1 piece at a time, roll out the dough on a floured surface into a 12-inch square, about 1/8 inch thick. Trim the edges to make an even square. Cut into about 15 strips using a fluted pastry wheel or a knife. Tie the strips into loose knots.
Working in batches, fry the dough knots until crisp, 2 to 3 minutes, returning the oil to 350 degrees F between batches. Remove with a slotted spoon or tongs and transfer to paper towels to drain. Combine the remaining 1 tablespoon cocoa powder and 1/3 cup confectioners¿ sugar in a bowl; dust both sides of the cookies using a sieve and let cool.