Soup Of Bitter Greens With Cheese Dumplings

Name: Soup Of Bitter Greens With Cheese Dumplings
Ingredients: 1 cup slightly packed freshly grated Parmesan cheese (4 ounces); 1 cup slightly packed freshly grated Pecorino Romano cheese (4 ounces), plus more for serving; 3/4 cup fine dry bread crumbs (3 ounces); 1 tablespoon finely chopped flat-leaf parsley; 4 large eggs, lightly beaten; 2 garlic cloves, minced; 2 tablespoons extra-virgin olive oil; 1/2 pound bitter greens, such as escarole or chicory, coarsely chopped; 2 quarts chicken stock or canned low-sodium broth; Salt and freshly ground pepper