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1
Make the chicken stock: Start with three drumsticks. Pull off most of the skin, using kitchen shears if that's easier, and then add them all to a big pot.
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2
Peel and halve both carrots, and throw those in too. Wash and roughly chop the celery, halve the onion, clean and chop the leek, and toss those into the pot too.
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3
Peel a nub of fresh ginger, cut it off, and add it to the pot. Add the: thyme, bay leaf, peppercorns, star anise and the clove. Fill the pot with water, so everything is covered liberally. (Remember, some water will evaporate in the cooking.)
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4
Bring the liquid to a boil, and then lower it to a simmer. Let the broth go for 2-21/2 hours, skimming the top occasionally, until it is tasty. Run the broth through a sieve, to remove all the solids. (Save the chicken! I put the drumsticks on a plate until they were cool, and then removed the meat. Cold chicken sandwiches with a Greek yogurt/smashed garlic/feta cheese spread make for a good lunch.)
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5
Make the butter: Let the butter soften slightly, and then put it in a bowl. Snip up most of the chives, and add them to the bowl. Mash the butter and chives together with a fork. If you will be eating soon, you can keep the bowl out. Otherwise, cover and refrigerate it.
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6
Prepare the soup: Wash and dry the scallions. Cut the whites twice lengthwise, in a cross, and then cut crosswise to separate them from the greens. (Basically, you want to cut each scallion into ribbons.) Set aside.
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7
Meanwhile, boil a pot of water. When the water reaches a boil, cook the Udon noodles based on the package instructions. Drain the noodles and set them aside.
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8
Set a medium fire under the pot of broth. Add the scallion ribbons and simmer the soup for about 5 minutes, or until the scallions are soft and lose a little of their oniony edge. Add the Udon noodles to the pot of broth.
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9
Just before you are ready to eat, add the four eggs to the soup, dropping one into each quadrant of the pot, so they don't touch as they cook. This is easy poaching! The noodles and scallions should keep the eggs in place. Cover the pot with a lid, and let the eggs cook for about 4 minutes, or until the whites are set.
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10
Run the remaining ginger through a mircroplane grater. Cut the lime into four slices. Snip up the remaining chives.
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11
Empty the soup into individual bowls, spooning one egg into each bowl. Garnish with the ginger, lime and chives.
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12
Swipe the chive butter onto the Pane Siciliano (toasted or not, whatever you prefer) and serve it with the soup.
