Step 1Heat the oven to 350 degrees. Heat the butter and olive oil in a 5 1/2-quart Dutch oven over medium heat. Add the onion, celery, carrot and rosemary. Cook until soft and browned, 7 minutes. Remove to a bowl. Add the meat to the pan, in batches, and brown on both sides.
Step 2Return the vegetables and all of the meat to the Dutch oven and season the meat with 1/2 teaspoon of salt. Cover the pan and place in the oven. Roast 30 minutes. Turn the meat over, and, if the pan looks too dry, add a little water. Roast until the meat is very tender, 30 minutes.
Step 3Remove the pan from the oven and place the meat in a bowl until cool enough to handle, reserving the juices in the pan and discarding the rosemary. Remove the meat from the bones; discard the bones. Place the meat in the bowl with the vegetables.
Step 4Set the pan on the stove and heat the juices to a simmer. Add the spinach and cook until it wilts, 2 minutes. Remove it with a slotted spoon, squeeze out the excess liquid, and add to the meat and vegetables. Reserve the juices for the pasta sauce.
Step 5Pass the meat and vegetables through a meat grinder or food grinder attachment fitted to a mixer (the holes should be about the diameter of a pencil). Place in a bowl. Let cool slightly, then combine with the Parmesan, salt to taste and pepper and nutmeg. Remove one-fourth of the filling for the agnolotti and combine it with the beaten egg; reserve the rest for another use.
Step 1Place the flour, egg and yolks in a food processor. Process, adding water a little at a time, until the dough clumps together. Remove to a work surface and form into a ball. Knead until smooth and elastic, 3 minutes.
Step 2Divide the dough into 4 parts and cover with plastic wrap. Working one piece at a time, pass the dough through the widest setting of a pasta machine, folding the dough into thirds the first time. Continue putting the dough through each setting until you reach the second-to-thinnest setting. Lightly dust the machine or dough with flour if it sticks. The pasta will be very thin and translucent. Cut the pasta strip in half crosswise and cover one piece with plastic wrap. Lay the other on a lightly floured wooden board in front of you.
Step 1To fill the pasta, place 1/2 teaspoon of filling at 3/4-inch intervals, 1 inch from the edge, along the length of the pasta. Fold the pasta over the filling lengthwise, making sure there's at least 1/2 inch from the edge of the fold to the beginning of the filling. Press down along the back edge with the side of your thumb to seal. With both hands, pinch between each dot of filling, thumbs in front, index fingers behind, so that the sides of each ball of filling form a vertical pleat. With your thumbs, press along the front.
Step 2With a ravioli cutter, cut around the pasta to form a decorative edge, then cut between the filling, always front to back, to form the agnolotti. Place the pasta on a baking sheet lined with a cotton dish towel sprinkled with flour. Repeat with the remaining pasta.
Step 3Bring a large pot of water to boil. Add salt. Cook half the agnolotti at a time until al dente, 4 to 6 minutes. Drain. Heat the reserved meat juices from the pan with the butter and sage leaves. Toss with the pasta and serve, passing the Parmesan on the side.