Prepare several baking sheets or platters, half of them with a light dusting of flour, the other half lined with paper towel. Set aside.
Place the egg yolks and whites in a large mixing bowl and beat well. Add the baking powder to the eggs. Gradually add the flour, combining it with the egg until you can knead it into a smooth dough.
Turn the dough out onto a lightly floured, large cutting board or clean, dry, flat surface. Break off a piece of the dough, roll it into a long 1/2- inch diameter strand and cut the strand into 3/4-inch pieces. With floured hands, roll each piece into a ball and place on the prepared cookie sheet or platter. Continue in this manner until all of the dough has been rolled into balls.
Heat the oil in a 6-quart pot over medium heat until hot, 375°F on a deep-fry thermometer. Working in batches, without crowding the pot, add some of the balls to the hot oil. Fry the dough for about 2 to 3 minutes, turning it gently until golden brown. Transfer the dough, using a slotted spoon, to paper towel-lined baking sheets or platters to drain and cool. Continue in this manner until all of the dough is fried. Make sure to maintain the oil temperature before adding the next batch.
Combine the honey, anisette, tangerine or orange juice, and the sliced rind in another 6-quart pot. Place over medium heat and bring to a boil. Add all of the dough balls in manageable amounts, bathing them in the honey mixture. When all are well coated, scoop out, drain, and pile onto a favorite platter in the shape of a mound. When cooled, top with rainbow colored nonpareil and shaved almonds.