Mini Muttballs and Ditalini

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6 cups chicken broth

Salt

3/4 pound ground beef, pork and veal mixture

2 large eggs

1/3 cup chopped shredded carrots

1/3 cup grated Parmigiano-Reggiano, plus more for sprinkling

1/3 cup bread crumbs

1/4 cup finely chopped fresh parsley leaves

1 clove garlic, mashed into a paste with a little salt, optional

Freshly ground black pepper

1/2 pound ditalini pasta