Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper or silicone baking mats.
In a mixer, beat the eggs and yolks until pale and fluffy. Slowly stream in the granulated sugar, melted butter and vanilla, and continue to mix until smooth.
Add the flour, baking powder and salt, and continue to mix on low until everything comes together in a firm dough.
On a lightly floured wooden board, briefly knead the dough to make a smooth ball, then pat into a rectangle and cut into 4 equal pieces. Split the pieces in half again to make 8 pieces, then repeat to make 16 equal dough balls. Set aside to make room to roll them.
Use your fingers to gently roll out each dough ball into a 12-inch rope; if the dough is excessively sticky, dust your hands very lightly with flour, then knead the dough for about 20 seconds. (If you use too much flour the dough will become brittle, so go easy on it.)
Cut each rope into three 4-inch sections, pinch the ends together to make rings, and place on the prepared baking sheets about 3 inches apart. Brush the tops with milk and sprinkle with sanding sugar.
Bake the cookies, rotating halfway through, 16 to 18 minutes. Let cool on racks, 20 minutes. The cookies will last for 10 days in an airtight container.
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