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Step 1
Preheat the oven to 400°F. Put the duck bits in a large roasting pan and drizzle a little oil over them. Mix to coat, then salt well. Roast until nicely browned, about 45 minutes to an hour.
Step 2
Move the roasted duck pieces to a large stockpot, add the roughly chopped chicken or duck feet and cover with cool water by 2 inches. The reason you use feet in this stock is for their collagen, which adds a tremendous amount of body to the broth. A pig's foot will do the same thing. Bring the stock to a gentle simmer and cook for at least 2 hours, and up to 8 hours if you'd like. Do not let it boil.
Step 3
Add the vegetables, herbs and spices and simmer gently for another 90 minutes to 2 hours. Turn off the heat.
Step 4
To strain your broth, set a strainer over a large container and put a paper towel or cheesecloth inside the strainer. Ladle the broth from the stockpot into the large container through the strainer. Keep doing this until you get to the bottom of the pot. Do not pour the pot into the container and do not try to get the last inch or so of broth from the pot -- if you do this, you will cloud your broth, and a clear broth is what we are looking for.
Step 5
Chill the broth and set in the fridge. You can make the broth up to 5 days ahead of time before you need to freeze it.
Step 6
In a large bowl, mix together all the ingredients and add salt to taste. Keep chilled until ready to use. You can make this a hour or two in advance.
Step 7
Get out a baking sheet and sprinkle semolina flour or cornmeal on it. This is for your completed cappelletti.
Step 8
Whisk together all the flours with the salt. Make a well in the center and crack the eggs inside. Using a fork, beat the eggs and then incorporate the flour until you get a shaggy mass. Get all the flour off the fork and switch to your hands. Knead the dough for 4 to 6 minutes, then coat with a little oil. Wrap tightly in plastic wrap and let the dough rest for 1 to 2 hours on the counter.
Step 9
Cut the dough into 4 equal pieces. Start with one and leave the others under the plastic wrap. Roll the dough out thin; on my Atlas machine I go to No. 7, where No. 9 is the thinnest.
Step 10
Get a small bowl of cool water handy. Use a 3-inch circle mold, or a wineglass, to cut out circles of dough. Put about a teaspoon of filling in the center. Dip your finger into the water and moisten the top half of each circle. Fold the pasta into a half-moon and seal it.
Step 11
To make a cappelletto, moisten one sealed end of the half-moon with a little water. Fold both ends back towards each other, letting the sealed part on the top of the "moon" fold upwards. Press the ends of the "moon" together with your fingers to seal. Repeat until you're done.
Step 12
Bring to a simmer enough broth to feed everyone (the recipe makes more than a gallon, so you will have plenty). Drop the heat to its lowest setting to just keep the broth warm. Don't let it boil.
Step 13
Fill your largest stockpot 3/4 full of water and bring it to a boil. Add a palm's worth of salt to the water; you need more salt than you might think to cook pasta. The water should taste like the sea.
Step 14
Boil the cappelletti until they float, and then for 1 more minute. Arrange them in shallow bowls for everyone and ladle over the broth. Garnish with minced chives or parsley.