In a large bowl, add the room temperature egg whites with the vanilla extract, almond extract, and orange zest.
Whisk with an electric whisk until you get a foamy consistency. It should not be stiff like meringues but very soft foam.
Add the sugar and the almond flour and mix with a spoon until you get a paste. If crumbly, knead with your hands until the dough stays compactly together.
Dust a cutting board with powdered sugar and roll the dough into a thick cylinder, about 2 inches (5 cm) thick, then cut it into 1 inch (2.5 cm) chunks.
Flatten lightly the discs on the board, then give them an oval shape and coat them well with powdered sugar.
Set the Ricciarelli on a baking sheet, then lightly wet your fingers with water and wet the surface of each cookie (it should be just slightly wet, not drippy), then dust again with abundant icing sugar to coat them well. Tap lightly with dry fingers to smoothen the sugary surface.
Bake in the preheated oven for the first 5 minutes at 300°F (150°C), then 5 minutes at 340°F (170°C) and the last 5 minutes at 320°F (160°C). Alternatively, you can bake them only at 320°F (160°C) for 18-20 minutes.
Gently move the cookies to a cooling rack with a spatula and let them cool completely before serving.
Notes
You can store Ricciarelli in a cookie tin in a dry cool place for 1-2 weeks.