Combine and mix well both types of flour with the sugar and the baking powder in a mixing bowl. Add the beaten egg and water to the flour mixture and combine well. The dough should be soft but dry. If the flour does not form a dough add a few tablespoons of water. Let the dough rest for about 10 minutes.
Put the sesame seeds in one shallow bowl and clean water in another. Pinch a small portion of the dough and form into a ball about ½ inch in diameter. Continue to make dough balls until all the dough is used. Pick up a dough ball and dip it in the water, then roll it in the sesame seeds to coat. Repeat for each dough ball.
Heat the vegetable oil in a wok until it is just beginning to simmer, or the temperature reaches 350° F. Fry the dough balls in batches of ten over medium heat. Fry the dough for about 10 minutes or until the balls crack and are golden brown. Lower the heat slightly if the dough is browning too quickly. Remove the dough balls from the oil and drain them on a paper towel. Repeat the frying process until all the dough balls are cooked.
Let cool for 20 minutes before serving.