Melt the butter in a 26 cm / 10-inch skillet over medium heat. Add the pork loin and brown on all sides, about 5 minutes.

Lower the heat, cover, and cook for 20 to 25 minutes, turning once, until the pork reaches 160 F / 71 C internally and flakes easily with a fork. Let it cool completely.

Finely chop the cooled pork with the prosciutto and mortadella by hand or in short pulses in a food processor, until the mixture looks like coarse crumbs, not a paste.

Transfer to a bowl and mix in the parmigiano, the filling egg, nutmeg, lemon zest, a pinch of salt, and black pepper. Cover and chill for 30 minutes so it firms up.

Mound the flour on a board or in a large bowl and make a well in the center. Crack in the 3 dough eggs and mix with a fork, gradually pulling in flour from the sides.

Knead by hand for 8 to 10 minutes until the dough is smooth and springs back when pressed. Wrap in plastic and rest at room temperature for 30 minutes.

Roll the dough into thin sheets, about 1 mm thick, using a pasta machine or rolling pin. Keep unused dough covered so it doesn't dry out.

Cut the sheets into 4 cm squares with a knife or pastry cutter.

Place 1/2 tsp of filling in the center of each square. Fold into a triangle and press the edges to seal, then wrap the triangle around your fingertip and pinch the two points together to form the cappelletto ring.

Arrange the shaped cappelletti in a single layer on a floured tray as you go, without stacking, so they don't stick together.

Bring the broth to a gentle simmer in a 6-quart / 5.5 L stockpot.

Slide the cappelletti into the simmering broth in batches so the pot isn't crowded. Cook for 4 to 5 minutes until they float and the pasta is tender at the edges but still holds its shape.

Ladle the broth and cappelletti into bowls, top with grated parmigiano, and serve right away.