1. Whisk to combine flour, baking powder, and salt in a bowl. In a separate bowl, beat eggs, egg yolks, and granulated sugar with an electric mixer on medium-high speed until pale and thick, 3 to 4 minutes. Mix in brandy and zests. Reduce speed to low; gradually add flour mixture. Beat just until dough comes together. Transfer to a lightly floured work surface, and knead until dough springs back slightly when pressed, about 2 minutes. Divide dough in half; wrap each in plastic. Let rest 1 hour at room temperature.

2. On a lightly floured surface, roll out half the dough into a rectangle less than 1/8 inch thick. Using a sharp knife or pastry wheel, cut dough into strips of varying widths and lengths, 1/4 to 1/2 inch wide and 5 to 6 inches long. For a branchlike effect, use a paring knife to split each strip about 1 inch from each end, if desired. Cover with a clean kitchen towel to keep dough from drying out. Repeat with remaining dough.

3. Heat oil in a large heavy Dutch oven or pot until it registers 360 degrees on a deep-fry thermometer. Gently pull each dough strip to stretch it almost double in length before carefully dropping in oil. Fry about 4 strips at a time, turning occasionally with a mesh skimmer, until they are golden and crisp, 2 to 3 minutes. Drain on paper towels, and repeat until all twigs are fried, carefully adjusting heat to maintain temperature as needed. Before serving, dust twigs generously with confectioners' sugar. Cookies are best eaten the same day they are fried (do not cover).