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Preheat the oven to 350 F. Prepare 4 baking sheets (or prepare 2 at a time) by lining with parchment paper or silicone mats. Set aside.
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Whisk together the four, baking powder and salt in a medium sized bowl. Set aside.
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Whisk the eggs in a large bowl until broken up and completely incorporated (i.e., no separate yellows or whites). While whisking, pour the sugar into the eggs in a thin stream.
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Pour the butter into the eggs, while whisking, in a thin stream.
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Whisk in the vanilla and fiori di sicilia.
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Gently fold the flour mix into the egg mixture. When it is mostly cohesive but still a little crumbly, turn it out onto a clean surface (lightly flour the surface unless you are using a silicone mat, in which case it will not need it).
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Briefly knead the dough to make it a cohesive ball.
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Divide the dough into 8 equal sized portions. Then divide each portion in half.
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With each portion (1/16 of the dough), roll it into an even rope 8 inches long. Then pinch the ends together to form a circle.
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Bake 4-6 circles of dough on a sheet at a time. If you bake 2 at once, be sure to rotate top to bottom and front to back halfway through baking (unless you are using a convection oven). Bake for 26-30 minutes, or until quite puffed and a deep golden brown.
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Remove to cool on the cookie sheet. If you need the cookie sheet for another round of baking, let cool for 5-7 minutes and then remove to a cooling rack.
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Do not ice the cookies until they are completely cooled.
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Whisk the lemon juice, vanilla and fiori di sicilia into the powdered sugar. Then add enough water, by the tablespoon, until you get a smooth and drippy yet thick icing.
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Dip the top half of each cookie into the icing. Let some of the excess drip off back into the bowl. Then scatter sprinkles over the icing and let set completely.