This is a Sunday supper, not something to be thrown together in minutes. The broth takes time to make, as do the tortellini. But once made, you can store the broth in the fridge a week, and the tortellini freeze well for a couple months. So you can make this a quick weeknight meal once you have everything in hand. Traditionally you'd use a leftover roast chicken carcass and leftover meat to make this recipe. But any white-meat bird (or rabbit, for that matter) will be just as good. Note that you can do something like this with red meat animals like venison and duck, but that's a different dish; the golden color here is important. Other birds to do this with would be pheasants, turkey, ruffed grouse, partridges or quail. Just remember you will need about the equivalent in weight to a big roast chicken, so you might need a dozen quail or so if you did it with that.
Start by making the broth. This recipe assumes you roasted the chicken or other game bird at some point earlier. If you haven't, and you are using uncooked carcasses, you will need to roast them at 400°F until nicely browned, which will take about an hour. Once you have roasted carcasses, hack or chop them into pieces with a cleaver or poultry shears and put them in a pot. Cover the carcasses with water by about 1 inch and bring to a gentle simmer. Don't let this boil. Partially cover the pot so some steam can escape, but so the broth doesn't reduce too much.
Let the chicken simmer very gently for at least 2 hours, and up to 4 hours. When you think you are about 90 minutes away from being done, add all the remaining broth ingredients except for the salt. Simmer for 90 minutes, then strain the broth.To get maximum clarity, a) don't let the broth boil at all during the whole process, and b) strain it through a paper towel set into a strainer by ladling the broth through, not dumping the contents of the pot into the strainer. This is how I got my broth so clear without going through the rigamarole of clarifying it with a raft like a French consomme. Clean the pot and pour the strained broth into it and set it under low heat. Don't let it boil! Add salt to taste.
While the broth is simmering, made the pasta dough. Pour the flour into a large bowl and make a well inside. Put the eggs and yolks into the well and mix to make a dough. Knead for at least 5 minutes and up to 10 minutes. Wrap in plastic wrap and let the dough rest for 1 hour. BUT... if you have a vacuum sealer, you can seal the dough in a vac-bag and it will hydrate instantly, no need to rest. I do this because making the tortellini is time-consuming.
Make the filling. Mix the chicken, lemon zest, cheese and nutmeg in a bowl. Taste it. It might not need more salt because the cheese is salty. Add salt if you need to, then put everything in a food processor with the egg. Pulse until you have a paste. Remember this filling is going into little tortellini, so it needs to be fairly smooth.
Now it's time to make the tortellini. Get a good work surface ready: I use a big maple board, but any large, clean surface will work. Set a little bowl of water near you, to paint the edges of the tortellini with your finger. Get something to cut the tortellini: A ruler and a knife is good, as you will be cutting squares of dough here. I actually use a square cookie cutter, which makes things go much faster. Stuff the tortellini filling into a sturdy plastic bag and squeeze it into a corner. Snip off the corner so you can use the plastic bag like a fancy pastry piping bag.
Cut your dough into about 8 pieces or so. Keep all the dough you're not using wrapped in plastic. Roll the dough out to No. 7 or No. 8 on your pasta roller; on my Atlas No. 9 is the thinnest setting. Cut out the squares of pasta. How large? Tortellini are supposed to be small, so about 1 1/2 inches if you can. If your fingers are too big to manage those little tortellini, make them larger.
Pipe about 1/2 teaspoon in the center of the square, about the size of a bean. You'll figure out how much is correct as you go. Fold the square over to make a triangle -- you'll need to paint the edges with water after the first couple of tortellini, as the dough dries quickly. Make sure there's no air in the triangle. Now fold the triangle around your forefinger and pinch together the edges. Set each tortellino on a baking sheet you've dusted with either semolina flour or cornmeal. Keep at it until you've used all the filling. This takes me about 2 hours, which is a fair bit of time, but your broth needs to cook anyway.
To finish, boil the tortellini in a large pot of salty water -- not the broth, as the starch from the pasta will cloud the broth. When the tortellini float to the surface, let them cook another 30 seconds, then drop a bunch in everyone's bowl. Pour the hot broth over the tortellini and garnish with something green, like parsley leaves.
Real tortellini are small, so make them small if you want to approach authenticity. But honestly, if it's easier for you to make the larger tortelli, which are twice the size of the tortellini in these pictures, go for it.