Preheat the oven to 190C/375° F.
Whisk together the sugar and eggs in a large bowl until lightened and foamy. Then whisk in the melted butter, a little at a time, followed by the lemon and orange zests.
In a separate bowl, whisk together the flours, baking powder and a tiny pinch of salt. Pour this into the wet ingredients and stir with a spatula until well incorporated. Knead briefly with your hands to form a cohesive dough.
Divide the dough into 16 pieces weighing about 40g (1½ ounces) each.
On a lightly floured work surface, roll each piece into a fat finger about 16cm (6 inches) long, then bend each finger it into an S shape.
Arrange the cookies on the baking sheet lined with parchment paper.
Brush the cookies with the egg, beaten together with a tablespoon of water. Then sprinkle them with sugar.
Bake for 20 to 25 minutes, until the serpette are set and golden in color, with a few light cracks on top.
Let your serpette cool, still on their baking sheet, for about 20 minutes, then transfer them cookies from the baking sheet to a wire rack to cool completely.