In a medium bowl, sift together the flour, baking powder and salt; set aside.
In a large bowl, lightly beat the eggs. Stir in the oil and anise flavoring and beat or whisk to combine.3. Gradually add the flour, mixing until the dough is stiff enough to be turned out of the bowl.
Turn the dough out onto a lightly floured surface and knead until the dough is smooth and pliable, kneading in any remaining flour mixture. Shape into a ball and divide into quarters. Wrap each tightly in plastic wrap and let rest for 30 minutes.
Meanwhile, fill a wide pan (I used a cast iron skillet - you could also use a Dutch oven) with at least one inch of oil and place over medium-high heat. The oil is hot enough when a little piece of dough dropped into the oil sizzles immediately.
Working with one portion of dough at a time and keeping the remainders covered, roll it out as thinly as possible and cut into 1½ to 2-inch wide strips. You can twist the dough, if you'd like. Drop the pieces of dough into the oil, being sure not to overcrowd the pan. Fry until light brown on the bottom side (1 to 2 minutes), then turn over and fry until the other side is also light golden brown. Remove to a wire rack placed over a double layer of paper towels and allow to drain. Repeat with the remaining dough. Dust with powdered sugar and serve. These can be made up to a week in advance and stored at room temperature in a tin or airtight container.