Step 1

Heat the oven to 300°F with a rack in the middle position. Distribute the bread on a rimmed baking sheet. Toast in the oven, stirring occasionally, until dried and crisp but not browned, 25 to 30 minutes. Cool completely.

Step 2

Meanwhile, in a large saucepan over medium, heat the oil until shimmering. Add the onion and ¼ teaspoon salt; cook, stirring occasionally, until translucent and softened, 4 to 6 minutes. Transfer to a large bowl; reserve the pot.

Step 3

In a food processor, pulse the cooled toasted bread until mostly fine with a few pea-size pieces, 15 to 20 pulses; you should have about 1½ cups. Add the breadcrumbs to the onion in the bowl, followed by the milk, eggs, nutmeg, ¼ teaspoon salt and ½ teaspoon pepper; let stand for about 5 minutes to hydrate.

Step 4

To the mixture, add the mortadella, Parmesan and parsley. Using a silicone spatula, mix until homogeneous, soft and sticky. Let rest at room temperature for 15 minutes. Meanwhile, in the saucepan, bring the broth to a simmer over medium; reduce to low and cover to keep warm. Put the flour in a wide, shallow bowl or a pie plate.

Step 5

After the dumpling mixture has rested, uncover the broth and return to a simmer over medium. Divide the dumpling mixture into 8 portions, each about ⅓ cup, rolling each portion into a ball between the palms of your hands (it’s fine if they do not form perfect spheres); place them on a plate. If the mixture is sticky, lightly moisten your hands with water to prevent sticking.

Step 6

One at a time, coat the balls on all sides with the flour, shake off excess and lower into the broth. Once all the dumplings are in the pan, return the broth to a simmer and cook, uncovered and occasionally stirring and turning the dumplings, until the dumplings float to the surface, about 10 minutes.

Step 7

Taste and season the broth with salt and pepper. Ladle the broth and dumplings into individual bowls, then sprinkle with additional parsley and Parmesan.