Start the broth: Put the water, whole chicken, beef shank, beef marrow bones, onion, carrot, celery, and black peppercorns in a large pot. Bring to a bare simmer over medium heat, 20β30 minutes, skimming foam. Adjust to maintain a gentle simmer and cook uncovered until the broth tastes rich and the meats are very tender, 2.5β3.5 hours.
Strain and season: Strain the broth through a fine sieve into a clean pot. Discard solids. Skim excess fat if desired. Season the clarified broth with the kosher salt. Keep hot over low heat.
Make the filling: Melt the unsalted butter in a small skillet over medium heat. Add the pork loin and cook, turning once, until just cooked through and lightly browned, 5β7 minutes. Cool completely, then finely mince the pork with the prosciutto and mortadella (or pulse in a food processor, taking care not to puree). In a bowl, combine the minced meats with the Parmigiano Reggiano, the lightly beaten large egg, and the ground nutmeg to form a firm paste. Cover and chill 30 minutes.
Make the pasta dough: Mound the 00 flour on a board and make a wide well. Crack the 3 large eggs into the center and beat with a fork, gradually drawing in flour until a shaggy dough forms. Knead until smooth and elastic, 8β10 minutes. Wrap and rest at room temperature for 30 minutes.
Roll the dough: Divide the dough into 4 pieces. Working with one piece at a time (keep the rest wrapped), roll by machine or pin to a very thin sheetβabout 1/32 inch; on a machine, to setting 6β7. Lightly dust a tray and your work surface with the semolina flour.
Cut and fill: Cut the sheet into 1.25-inch (3 cm) squares. Place about 1/4 teaspoon of filling in the center of each square. Fold into a tight triangle, pressing out air and sealing edges firmly.
Shape tortellini: Wrap each triangle around your fingertip, bringing the two tips together and pinching to seal. Set the tortellini on the semolina-dusted tray in a single layer and cover with a towel. Repeat with remaining dough and filling.
Cook and serve: Bring the seasoned broth to a gentle boil. Add tortellini in batches and simmer until they float and the edges are tender but still slightly firm, 2β4 minutes. Ladle tortellini and hot broth into warm bowls and serve immediately.